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Index to OEIS: Section Ph

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Index to OEIS: Section Ph


[ Aa | Ab | Al | Am | Ap | Ar | Ba | Be | Bi | Bl | Bo | Br | Ca | Ce | Ch | Cl | Coa | Coi | Com | Con | Cor | Cu | Cy | Da | De | Di | Do | Ea | Ed | El | Eu | Fa | Fe | Fi | Fo | Fu | Ga | Ge | Go | Gra | Gre | Ha | He | Ho | Ia | In | J | K | La | Lc | Li | Lo | Lu | M | Mag | Map | Mat | Me | Mo | Mu | N | Na | Ne | Ni | No | Nu | O | Pac | Par | Pas | Pea | Per | Ph | Poi | Pol | Pos | Pow | Pra | Pri | Pro | Ps | Qua | Que | Ra | Rea | Rel | Res | Ro | Ru | Sa | Se | Si | Sk | So | Sp | Sq | St | Su | Sw | Ta | Te | Th | To | Tra | Tri | Tu | U | V | Wa | We | Wi | X | Y | Z | 1 | 2 | 3 | 4 ]


phi : see golden ratio phi
phi(n) (A000010): see totient function phi(n)
Phi(n): A005728*
phi, Phi: A000108, A001006, A007477, A025262, A025268

pi(x), sequences related to :

pi(x), number of primes <= x: A000720*
pi(x), pi(10^n): A006880

Pi, sequences related to :

Pi, approximations of: A068028 = 22/7, A068079 = 355/113, A068089 = 104348/33215, [see also: convergents, continued fractions]
A216542 (Sum (-1)^(k-1)/(2k-1), k=1..5e4), A013706 (twice that), A216543 (4x that),
A216544 (Sum (-1)^(k-1)/(2k-1), k=1..5e5), A216545 (twice that), A013705 (4x that),
A216546 (Sum (-1)^(k-1)/(2k-1), k=1..5e6), A216547 (twice), A216548 (4 times), A195793 (arctan(10^6) ~ Pi/2 - 10^-6).
[See also: series for Pi].
Pi, continued cotangent for: A002667*
Pi, continued fraction for: A001203*; records therein: A007541, A033089, A033090.
convergents: A002485* / A002486*. [See also "approximations: 22/7, 355/113, ...]
Pi, decimal expansion of: A000796*, A011545: digits 1..n concatenated, A005042: primes therein; A092845: reverse(A011545), A007523: primes therein.
Pi in base b: A004601 (b=2), A004602 (b=3), A004603 (b=4), A004604 (b=5), A004605 (b=6), A004606 (b=7), A006941 (b=8), A004608 (b=9),
A000796 (b=10), A068436 (b=11), A068437 (b=12), A068438 (b=13), A068439 (b=14), A068440 (b=15), A062964 (b=16), A060707 (b=60).
Pi, Egyptian fractions for : A001466*, variants (essentialy the same): A182257, A224230. Pi = Sum 1/a(n) (signed): A001467. Egyptian fraction for 1/Pi: A006524.
Pi, decimal expansion of, related to : A001355: Pie, interlace digits of Pi and e, A058382: continued fraction of Pie,
A104691: interlace digits of e and Pi, A284155: continued fraction of ePi; A078424: mix digits of Pi, e and phi. A076790: mix digits of Pi and phi.
Pi, decimal expansion of, strings of digits in :
A037008 + 1 = A014976 (position of "0"s), A050201 (position of "00"s), A050202, A083598, A083599, A083600, A083601 (seven "0"s)
A037000 + 1 = A053745 (position of "1"s), A050208 (position of "11"s), A050209, A083602, A083603, A083604, A083605 (seven "1"s).
A037001 + 1 = A053746 (position of "2"s), A050215, A083606, A083607, A083608, A083609, A118079 (seven "2"s)
A037002 + 1 = A053747 (position of "3"s), A050222, A083610, A083611, A083612, A083613, A083614 (seven "3"s)
A037003 + 1 = A053748 (position of "4"s), A050230, A083615, A083616, A083617, A083618, A083619 (seven "4"s)
A037004 + 1 = A053749 (position of "5"s), A050238, A083620, A083621, A083622, A083623, A083624 (seven "5"s)
A037005 + 1 = A053750 (position of "6"s), A050245, A083625, A083626, A083627, A083628, A083629, A083630 (eight "6"s)
A036974 + 1 = A053751 (position of "7"s), A050254, A083631, A083632, A083633, A083634, A083635, A083636 (eight "7"s)
A037006 + 1 = A053752 (position of "8"s), A050263, A083637, A083638, A083639, A083640, A083641 (seven "8"s)
A037007 + 1 = A053753 (position of "9"s), A050272, A083642, A083643, A083644, A083645, A083646 (seven "9"s)
exactly k consecutive equal digits: A049518 (k=2), A049519, A049520, A049521, A049534 (k=6).
at least k consecutive equal digits: A049514 (k=2), A049515, A049516 (k=4), A049517 (k=5).
occurrences of '0123456789': A101815, of '9876543210': A101816.
Pi, decimal expansion of, strings of digits in, first occurrence of :
n consecutive equal digits: A049522 (exactly n), A049523 (at least n).
at least n times the same digit: A035117 ('1's), A050281 ('2's), A050282, A050283, A050284, A050286, A050287, A048940 ('9's).
exactly n times the same digit: A050279 ('0's), A096755 ('1's), A096756, A096757, A096758, A096759, A096760, A096761, A096762, A096763 ('9's).
concatenate(1,...,n): A121280(n) = A068987(n) - 1; first digits of e = 2.718...: A090898; digits of Pi in e: A115234.
the string n: A176341.
Pi, series for : A007514 (= A075874, essentially): Sum a(n)/n! = Pi. A005148, A005149, A006934: other series for Pi. [See also: Egyptian fractions for Pi]
Pi, see also: A002161: sqrt(Pi), A002388: Pi^2, A039661: e^Pi, A059850: Pi^e.

piano keyboard: A059620*, A079731, A060106, A060107, A081031, A081032
picture-perfect numbers: A069942
pieces: see also under partitions
Pierce expansions: A006275, A006276, A006283, A006284
Pierpont primes: see primes, Pierpont
Pisano numbers: see Pisano periods
Pisano periods: A001175*

Pisano periods, generalized: listed in R. J. Mathar, A Table of Pisano Period Lengths (1) A000032, A000034, A000045, A000051, A000073, A000129, A000213, A000225, A000285, A000290, A000292, A000578, A001045, A001060, A001075, A001076, A001175, A001333, A001353, A001519, A001590, A001608, A001644, A001834, A001906, A002532, A002533, A002605, A002878, A003462, A003665, A003688, A005248, A005668, A006012, A006130, A006131, A006138, A006190, A006355
Pisano periods, generalized: listed in R. J. Mathar, A Table of Pisano Period Lengths (2) A006495, A007070, A007482, A009116, A009545, A010892, A013655, A014551, A014983, A015440, A015441, A015442, A015443, A015518, A015519, A015521, A015523, A015530, A015531, A015532, A015535, A015537, A015540, A015541, A015551, A015564, A015568, A015574, A015576, A015580, A015584, A015587, A015591, A016116, A020695, A020701, A020712, A020992, A021006, A022086
Pisano periods, generalized: listed in R. J. Mathar, A Table of Pisano Period Lengths (3) A022095, A022097, A022098, A022099, A022100, A022101, A022102, A022103, A026150, A028859, A030195, A038608, A038754, A046717, A046738, A048573, A048693, A048694, A049347, A052533, A052918, A054490, A055099, A056594, A057079, A057087, A057088, A057597, A057681, A061084, A061347, A063727, A072263, A072265, A077917, A077957, A077966, A077985, A078008, A078020
Pisano periods, generalized: listed in R. J. Mathar, A Table of Pisano Period Lengths (4) A078069, A083099, A083858, A085750, A087451, A090132, A090591, A094359, A098149, A098150, A099087, A099843, A104217, A104769, A104934, A105476, A106291, A106293, A107920, A108520, A110512, A122994, A123335, A125905, A130472, A132429, A164539, A174191, A175181, A175182, A175183, A175184, A175185, A175286, A175289, A175290, A175291, A186646

Pisot sequences, sequences related to :

Pisot sequences, definitions: A008776*
Pisot sequences, warning about recurrences for: A010925
Pisot sequences: ( 1) A000302, A000351, A000400, A000420, A001018, A001019, A001519, A004171, A007283
Pisot sequences: ( 2) A007699, A008776 (has Maple code for most variants), A009056, A010900, A010901, A010902, A010903, A010904, A010905, A010906, A010907
Pisot sequences: ( 3) A010909, A010910, A010911, A010912, A010913, A010914, A010915, A010916, A010917, A010919, A010920
Pisot sequences: ( 4) A010924, A010925, A011557, A014001, A014002, A014003, A014004, A014005, A014006, A014007, A014008
Pisot sequences: ( 5) A018920, A019492, A020695, A020696, A020698, A020701, A020702, A020704, A020705, A020706
Pisot sequences: ( 6) A020708, A020709, A020710, A020711, A020712, A020713, A020714, A020715, A020716, A020717, A020718
Pisot sequences: ( 7) A020720, A020721, A020722, A020723, A020727, A020728, A020729, A020730, A020732, A020734, A020735
Pisot sequences: ( 8) A020736, A020737, A020739, A020741, A020742, A020743, A020744, A020745, A020746, A020747, A020748, A020749
Pisot sequences: ( 9) A020750, A020751, A020752, A021000, A021001, A021004, A021006, A021008, A021011, A021013, A021014, A048575
Pisot sequences: (10) A048576, A048577, A048578, A048579, A048580, A048581, A048582, A048583, A048584, A048585, A048586, A048587
Pisot sequences: (11) A048588, A048589, A048590, A048591, A048592, A048624, A048625, A048626, A051016, A051017
Pisot sequences E: A000079 (1,2), A000244 (1,3) and (3,9), A007484 (2,7), A007699 (10,219), A008776 (2,6), A010914 (5,17), A020707 (4,8), A020719 (7,8), A020695 (2,3), A020701 (3,5), A020706 (4,6), A020720 (7,9), A020729 (2,10). A010908 (4,21)
Pisot sequences L: A000079 (1,2) A000051 (2,3) A000244 (1,3) (3,9) A008776 (2,6) A018910 (4,5) A018913 (1,9) A018918 (3,6) A018919 (3,9) A020706 (4,6) A020707 (4,8) A020729 (2,10) A020737 (5,9) A048577 (3,4) A048578 (3,5)
Pisot sequences P: A000079 (1,2) A000244 (1,3) (3,9) A008776 (2,6) A020701 (3,5) A020707 (4,8) A020719 (7,8) A020720 (7,9) A020727 (2,7) A020729 (2,10) A021006 (4,11)
Pisot sequences S (Shallit): A018902 (1,4) A018903 (1,5) A018904 (1,6) A018906 (2,6) A018907 (2,7) A018908 (3,4) A018909 (3,6) A022019 (2,32) A022021 (5,20) A022022 (5,45) A022023 (6,30)
Pisot sequences T: A000079 (1,2) A000244 (1,3) (3,9) A008776 (2,6) A010920 (3,13) A010922 (14,23) A018914 (2,5) A018915 (2,6) A018916 (2,8) A018917 (3,5) A018920 (3,10) A020707 (4,8) A020719 (7,8) A020729 (2,10)

planar , sequences related to :

planar graphs: see graphs, planar
planar vs plane: some authors make a distinction between "plane", meaning embedded in the plane with a distinguished exterior region, and "planar", meaning embedded in the sphere (with no distinguished region)

Planck's constant: A003676
plastic constant: A060006
plastic number: A060006
plots, misleading: see deceptive plots
plots, sequences with interesting: see graphs (or plots), sequences with interesting
plus perfect numbers: A005188*


[ Aa | Ab | Al | Am | Ap | Ar | Ba | Be | Bi | Bl | Bo | Br | Ca | Ce | Ch | Cl | Coa | Coi | Com | Con | Cor | Cu | Cy | Da | De | Di | Do | Ea | Ed | El | Eu | Fa | Fe | Fi | Fo | Fu | Ga | Ge | Go | Gra | Gre | Ha | He | Ho | Ia | In | J | K | La | Lc | Li | Lo | Lu | M | Mag | Map | Mat | Me | Mo | Mu | N | Na | Ne | Ni | No | Nu | O | Pac | Par | Pas | Pea | Per | Ph | Poi | Pol | Pos | Pow | Pra | Pri | Pro | Ps | Qua | Que | Ra | Rea | Rel | Res | Ro | Ru | Sa | Se | Si | Sk | So | Sp | Sq | St | Su | Sw | Ta | Te | Th | To | Tra | Tri | Tu | U | V | Wa | We | Wi | X | Y | Z | 1 | 2 | 3 | 4 ]


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