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Search: author:gerasimov name:becomes
Displaying 1-10 of 36 results found. page 1 2 3 4
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A143717 (1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13, 2*7, 3*5,..) becomes (abs(1-2-3, 2-2-5, 2-3-7, 2-3-3, 2-2-5, 11-2-2, 3-13-2, 7-3-5,..)). +0
5
4, 5, 8, 4, 5, 7, 12, 1, 19, 3, 15, 5, 32, 4, 1, 7, 7, 24, 28, 9, 20, 3, 36, 20, 8, 38, 47, 11, 4, 68, 5, 3, 0, 13, 42, 5, 6, 15, 86, 3, 58, 26, 1, 10, 75, 17, 22, 73, 4, 73, 29, 2, 1, 14, 73, 2, 122, 3, 15, 44, 24, 80, 4, 8, 24, 18, 16, 95, 7, 10, 5, 101, 117, 14, 9, 158, 3, 108, 9, 31 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Table of n, a(n) for n=1..80.
EXAMPLE
Abs (7-3-5)=abs (-1) =1=a(8).
Abs (2-4-17)=abs(-19)=19=a(9).
Abs (2-3-2)=abs (-3)=3=a(10).
Abs (19-2-2)=abs 15=15=a(11),
Abs (5-3-7)=abs (-5)=5=a(12),
etc.
CROSSREFS
Cf. A141287, A141261, A136678.
KEYWORD
nonn,less
AUTHOR
_Juri-Stepan Gerasimov_, Nov 13 2008
EXTENSIONS
Replaced a 56 by a 1. R. J. Mathar, Feb 21 2009
STATUS
approved
A136740 (0, 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3,..) becomes (2, 3, 5, 7, 11^13, 17, 19*23, 29, 31^37, 41^43, 47*53, 59, 61^67*71,..). +0
4
2, 3, 5, 7, 34522712143931, 17, 437, 29 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Table of n, a(n) for n=1..8.
EXAMPLE
a(5)=11^13=34522712142931.
a(7)=19*23=437,
etc.
CROSSREFS
Cf. A141269, A141270, A143652, A143653, A143666.
KEYWORD
nonn,less
AUTHOR
_Juri-Stepan Gerasimov_, Nov 08 2008
EXTENSIONS
Corrected typo in a(5), inserted a(6). R. J. Mathar, Feb 21 2009
STATUS
approved
A143716 (0, 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3,..) becomes (1, 2, 3, 4, 5^6, 7, 8*9, 10, 11^12, 13^14, 15*16, 17, 18^19*20,..). +0
3
1, 2, 3, 4, 15625, 7, 72, 10, 313842837672, 393737638569928, 240, 17, 14164706907106753527152640 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The list of the bases and exponents of the prime factorizations is replaced by the list of positive integers, but the operations stay fixed. - R. J. Mathar, Mar 22 2016
LINKS
Table of n, a(n) for n=1..13.
EXAMPLE
a(5)=5^6=15625.
a(6)=7.
a(7)=8*9=72.
CROSSREFS
Cf. A141287, A141261, A136611.
KEYWORD
nonn
AUTHOR
_Juri-Stepan Gerasimov_, Nov 13 2008
EXTENSIONS
Definition and terms corrected. - R. J. Mathar, Mar 22 2016
STATUS
approved
A136611 (0, 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, ...) becomes (0, 1, 2, 3, 4^5, 6, 7*8, 9, 10^11, 12^13, 14*15, 16, 17^18*19, ...). +0
2
0, 1, 2, 3, 1024, 6, 56, 9, 100000000000, 106993205379072, 210, 16, 267198604589286774829171, 20, 462, 552, 2220446049250313080847263336181640625, 27 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
a(36) has 8261 decimal digits.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..35
EXAMPLE
a(4) = 4^5 = 1024,
a(6) = 7*8 = 56,
a(8) = 10^11 = 100000000000,
a(9) = 12^13 = 19216339899072,
a(10) = 14*15 = 210,
a(12) = 17^18*19 = 266314164608823014829171,
etc.
MATHEMATICA
j = k = 0; f[n_] := Flatten@ Riffle[Map[If[#2 == 1, {}, {"~Power~"}] & @@ # &, FactorInteger[n]], "~Times~"]; Array[(j = k; k += #2 + 1; ToExpression@ Apply[StringJoin, Riffle[Map[ToString, j + Range[0, #2]], #1]]) & @@ {#, Length[#]} &@ f[#] &, 22, 0] (* Michael De Vlieger, Oct 24 2022 *)
CROSSREFS
Cf. A141269, A141270.
KEYWORD
nonn
AUTHOR
_Juri-Stepan Gerasimov_, Nov 08 2008
EXTENSIONS
a(9) and a(12) corrected and 2 terms appended by R. J. Mathar, Apr 14 2010
Offset 0 from Michael De Vlieger, Oct 24 2022
STATUS
approved
A141186 (1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, ...) becomes (2, 3, 5, 7^11, 13, 17*19, 23, 29^31, 37^41, 41*43, 53, 59^61*67, ...). +0
2
2, 3, 5, 1977326743, 13, 323, 23, 2159424054808578564166497528588784562372597429, 19782022283855446341112457192300036270147066771005176357387103237, 2021 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Table of n, a(n) for n=1..10.
EXAMPLE
a(5)=7^11=1977326743.
a(7)=17*19=323,
etc.
CROSSREFS
Cf. A141287, A141261, A143678.
KEYWORD
nonn,less
AUTHOR
_Juri-Stepan Gerasimov_, Nov 08 2008
EXTENSIONS
More terms from R. J. Mathar, Apr 14 2010
STATUS
approved
A143653 (0, 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13,..) becomes (0^(1*2), 3^(2*2), 5^(2*3), 7^(2*3), 3^(2*2), 5^(11*2), 2^(3*13),..). +0
2
0, 81, 15625, 117649, 81, 2384185791015625, 549755813888, 2097152, 390625, 24137569, 274877906944, 32768, 3909821048582988049, 148035889, 59049, 549755813888, 81, 10367793076318844190248738727596255138212949486449 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Table of n, a(n) for n=1..18.
EXAMPLE
0^(1*2)=0^2=0=a(1).
3^(2*2)=3^4=81=a(2).
5^(2*3)=5^6=15625=a(3).
7^(2*3) =7^6=117649=a(4).
3^(2*2)=3^4=81=a(5).
5^(11*2)=5^22=2384185791015625=a(6).
2^(3*13) =2^39=549755813888=a(7).
2^(7*3)=2^21=2097152=a(8), etc.
CROSSREFS
Cf. A141269, A141270.
KEYWORD
nonn,less
AUTHOR
_Juri-Stepan Gerasimov_, Nov 01 2008
EXTENSIONS
a(6), a(11) corrected, extended by R. J. Mathar, Nov 06 2008
STATUS
approved
A143710 (1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13, 2*7, 3*5,..) becomes (1+2+3, 2+2+5, 2+3+7, 2+3+3, 2+2+5, 11+2+2, 3+13+2, 7+3+5,..). +0
2
6, 9, 12, 8, 9, 15, 18, 15, 23, 7, 23, 15, 36, 8, 9, 19, 11, 34, 38, 19, 24, 11, 42, 24, 18, 48, 53, 15, 10, 72, 9, 11, 10, 21, 68, 11, 16, 29, 90, 7, 68, 36, 15, 20, 81, 21, 28, 83, 8, 77, 45, 6, 37, 18, 85, 12, 126, 7, 29, 48, 34, 102, 10, 22, 28, 80, 26, 105, 11, 16, 9, 105, 123 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Table of n, a(n) for n=1..73.
EXAMPLE
a(8)=7+3+5=15.
a(9)=2+4+17=23.
a(10)=2+3+2=7.
a(11)=19+2+2=23.
a(12)=5+3+7=15.
a(13)=2+11+23=36,
etc.
CROSSREFS
Cf. A141287, A141261, A136735.
KEYWORD
nonn,less
AUTHOR
_Juri-Stepan Gerasimov_, Nov 13 2008
EXTENSIONS
a(43) corrected by R. J. Mathar, Apr 14 2010
STATUS
approved
A143652 (0, 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13, ...) becomes (0^(1+2), 3^(2+2), 5^(2+3), 7^(2+3), 3^(2+2), 5^(11+2), 2^(3+13), ...). +0
1
0, 81, 3125, 16807, 81, 1220703125, 65536, 1024, 15625, 1419857, 2097152, 256, 96889010407, 6436343, 2187, 65536, 81, 157775382034845806615042743, 150094635296999121, 256, 61159090448414546291, 1953125, 32 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Table of n, a(n) for n=1..23.
EXAMPLE
0^(1 + 2) = 0^3 = 0 = a(1).
3^(2 + 2) = 3^4 = 81 = a(2).
5^(2 + 3) = 5^5 = 3125 = a(3).
7^(2 + 3) = 7^5 = 16807 = a(4).
3^(2 + 2) = 3^4 = 81 = a(5).
5^(11 + 2) = 5^13 = 1220703125 = a(6).
2^(3 + 13) = 2^16 = 65536 = a(7).
2^(7 + 3) = 2^10 = 1024 = a(8), etc.
MAPLE
pflat2 := proc(nmax) local a, ifs, n, p, c ; a := [0, 1] ; for n from 2 to nmax do ifs := ifactors(n)[2] ; for p in ifs do a := [op(a), op(1, p)] ; if op(2, p) > 1 then a := [op(a), op(2, p)] ; fi; od: od: a ; end: pL := pflat2(120) : for n from 1 to nops(pL)-4 by 3 do printf("%d, ", op(n, pL)^(op(n+1, pL)+op(n+2, pL)) ) ; od: # R. J. Mathar, Nov 06 2008
CROSSREFS
Cf. A141269, A141270.
KEYWORD
nonn
AUTHOR
_Juri-Stepan Gerasimov_, Nov 01 2008
EXTENSIONS
Extended by R. J. Mathar, Nov 06 2008
STATUS
approved
A143666 (0, 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13,..) becomes (0^1*2, 3^2*2, 5^2*3, 7^2*3, 3^2*2, 5^11*2, 2^3*13,..). +0
1
0, 18, 75, 147, 18, 97656250, 104, 384, 100, 867, 1048576, 96, 539, 1587, 486, 24576, 18, 6439811511626359453675214, 7533, 96, 2057, 156250, 16, 26011, 3188646, 9963, 56, 3698, 2662, 575, 8836, 4374, 64, 258280326, 434176, 24, 97656250, 6561, 10469 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
Table of n, a(n) for n=1..39.
EXAMPLE
0^1*2=0*2=0=a(1).
3^2*2=9*2=18=a(2).
5^2*3=25*3=75=a(3).
7^2*3=49*3=147=a(4).
3^2*2=9*2=18=a(5).
5^11*2=48828125*2=97656250=a(6).
2^3*13 =8*13=104=a(7).
2^7*3=128*3=384=a(8), etc.
CROSSREFS
Cf. A141269, A141270.
KEYWORD
nonn
AUTHOR
_Juri-Stepan Gerasimov_, Nov 01 2008
EXTENSIONS
Extended by R. J. Mathar, Nov 06 2008
STATUS
approved
A143677 ( 1, 2, 3, 2^2, 5, 2*3, 7, 2^3, 3^2, 2*5, 11, 2^2*3, 13,..) becomes (abs (1-2, 3-2, 2-5, 2-3, 7-2, 3-3, 2-2, 5-11, 2-2, 3-13,..)). +0
1
1, 1, 3, 1, 5, 0, 0, 6, 0, 10, 5, 2, 2, 15, 1, 17, 3, 4, 9, 21, 0, 3, 11, 0, 0, 22, 1, 26, 3, 8, 15, 2, 0, 1, 35, 16, 11, 2, 39, 4, 41, 9, 1, 3, 24, 2, 4, 0, 3, 14, 0, 40, 1, 2, 9, 4, 16, 27, 57, 1, 56, 29, 1, 5, 1, 11, 8, 65, 15, 20, 3, 64, 1, 1, 71, 34, 3, 0, 12, 9, 10, 77, 1, 1, 39, 81, 1, 2, 15 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
Table of n, a(n) for n=1..89.
EXAMPLE
Abs(1-2)=abs(-1)=1=a(1).
Abs(3-2)=abs(1)=1=a(2).
Abs(2-5)=abs(-3)=3=a(3).
Abs(2-3)=abs(-1)=1=a(4).
Abs(7-2)=abs(5)=5=a(5).
Abs(3-3)=abs(0)=0=a(6).
Abs(2-2)=abs(0)=0=a(7).
Abs(5-11)=abs(-6)=6=a(8).
Abs(2-2)=abs(0)=0=a(9).
Abs(3-13)=abs(-10)=10=a(10), etc.
MAPLE
pflat2 := proc(nmax) local a, ifs, n, p, c ; a := [1] ; for n from 2 to nmax do ifs := ifactors(n)[2] ; for p in ifs do a := [op(a), op(1, p)] ; if op(2, p) > 1 then a := [op(a), op(2, p)] ; fi; od: od: a ; end: pL := pflat2(300) : for n from 1 to nops(pL)-3 by 2 do printf("%d, ", abs(op(n, pL)-op(n+1, pL)) ) ; od: # R. J. Mathar, Nov 06 2008
CROSSREFS
Cf. A141257, A141261.
KEYWORD
nonn,less
AUTHOR
_Juri-Stepan Gerasimov_, Nov 01 2008
EXTENSIONS
Removed incompatibilities with internal OEIS format, extended, R. J. Mathar, Nov 06 2008
STATUS
approved
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Last modified April 25 01:35 EDT 2024. Contains 371964 sequences. (Running on oeis4.)