login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
Search: keyword:new
Displaying 1-10 of 423 results found. page 1 2 3 4 5 6 7 8 9 10 ... 43
     Sort: relevance | references | number | modified | created      Format: long | short | data
A371332 Decimal expansion of Sum_{k>=1} 1/(k^(1/4)*(1+k)). +0
0
3, 7, 4, 7, 8, 3, 4, 7, 4, 3, 8, 4, 4, 8, 8, 7, 5, 7, 7, 8, 8, 8, 0, 5, 4, 6, 3, 5, 8, 9, 7, 6, 9, 3, 7, 6, 6, 7, 1, 1, 4, 8, 7, 3, 3, 2, 7, 7, 7, 3, 0, 0, 8, 8, 7, 7, 9, 4, 5, 2, 9, 5, 6, 9, 2, 5, 5, 5, 4, 7, 4, 0, 7, 1, 2, 3, 4, 7, 3, 7, 6, 1, 1, 8, 8, 7, 1, 5, 2, 1, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
Equals Sum_{i>=0} (-1)^i*zeta(5/4+i).
EXAMPLE
3.7478347438448875778880546...
PROG
(PARI) sumalt(i=0, (-1)^i*zeta(5/4+i)) \\ Hugo Pfoertner, Mar 19 2024
CROSSREFS
Cf. A226317 (for k^1/2), A371331 (k^1/3), A371333 (k^1/5).
KEYWORD
nonn,cons,new
AUTHOR
R. J. Mathar, Mar 19 2024
STATUS
approved
A371333 Decimal expansion of Sum_{k>=1} 1/(k^(1/5)*(1+k)). +0
0
4, 7, 1, 9, 6, 1, 7, 5, 3, 8, 1, 6, 2, 6, 1, 4, 4, 8, 3, 6, 0, 5, 7, 8, 2, 7, 2, 4, 0, 0, 1, 3, 2, 3, 1, 1, 5, 4, 7, 5, 7, 1, 0, 5, 1, 1, 1, 9, 8, 2, 8, 4, 3, 7, 6, 6, 2, 1, 0, 8, 2, 5, 8, 5, 7, 0, 6, 2, 6, 4, 8, 6, 1, 3, 9, 2, 3, 1, 0, 8, 9, 1, 9, 0, 9, 4, 9, 2, 2, 2, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
Equals Sum_{i>=0} (-1)^i*zeta(6/5+i).
EXAMPLE
4.71961753816261448360578272400..
PROG
(PARI) sumalt(i=0, (-1)^i*zeta(6/5+i)) \\ Hugo Pfoertner, Mar 19 2024
CROSSREFS
Cf. A226317 (for k^1/2), A371331 (k^1/3), A371332 (k^1/4).
KEYWORD
nonn,cons,new
AUTHOR
R. J. Mathar, Mar 19 2024
STATUS
approved
A371331 Decimal expansion of Sum_{k>=1} 1/(k^(1/3)*(1+k)). +0
0
2, 7, 9, 0, 0, 1, 8, 2, 9, 3, 0, 9, 7, 1, 5, 3, 3, 2, 9, 9, 3, 3, 5, 6, 2, 7, 6, 2, 2, 0, 5, 3, 8, 7, 3, 4, 9, 5, 6, 2, 9, 3, 7, 3, 1, 5, 8, 4, 8, 4, 9, 2, 2, 4, 4, 1, 2, 4, 0, 0, 5, 8, 3, 8, 9, 2, 0, 8, 4, 6, 9, 0, 9, 0, 1, 0, 9, 4, 5, 4, 5, 3, 7, 7, 5, 8, 6, 1, 9, 2, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
Equals Sum_{i>=0} (-1)^i*zeta(4/3+i).
EXAMPLE
2.790018293097153329933562762205..
PROG
(PARI) sumalt(i=0, (-1)^i*zeta(4/3+i)) \\ Hugo Pfoertner, Mar 19 2024
CROSSREFS
Cf. A226317 (for k^1/2), A371332 (k^1/4), A371333 (k^1/5).
KEYWORD
nonn,cons,new
AUTHOR
R. J. Mathar, Mar 19 2024
STATUS
approved
A371334 Decimal expansion of zeta(4/3). +0
0
3, 6, 0, 0, 9, 3, 7, 7, 5, 0, 4, 5, 8, 8, 6, 2, 4, 2, 1, 2, 9, 2, 2, 0, 7, 5, 7, 8, 4, 7, 5, 4, 1, 1, 2, 7, 7, 5, 5, 6, 7, 7, 3, 3, 0, 0, 3, 3, 7, 5, 2, 5, 2, 6, 0, 9, 9, 1, 5, 7, 0, 0, 4, 2, 4, 2, 0, 5, 7, 0, 1, 5, 8, 1, 5, 4, 8, 7, 3, 6, 3, 3, 7, 1, 1, 6, 0, 2, 9, 8, 8, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
EXAMPLE
3.600937750458862421292..
MAPLE
Zeta(4/3) ; evalf(%) ;
PROG
(PARI) zeta(4/3) \\ Hugo Pfoertner
KEYWORD
nonn,cons,new
AUTHOR
R. J. Mathar, Mar 19 2024
STATUS
approved
A371335 Decimal expansion of zeta(5/3). +0
0
2, 1, 2, 3, 5, 2, 2, 9, 6, 8, 8, 5, 7, 5, 8, 3, 4, 9, 1, 5, 8, 7, 3, 7, 2, 5, 8, 8, 9, 7, 1, 2, 2, 9, 5, 3, 8, 1, 8, 5, 5, 4, 9, 6, 9, 0, 2, 1, 5, 0, 0, 9, 3, 3, 6, 8, 4, 7, 0, 1, 0, 0, 2, 9, 8, 9, 2, 7, 6, 1, 5, 3, 6, 6, 5, 8, 8, 2, 1, 9, 6, 7, 2, 4, 4, 5, 4, 8, 7, 8, 4, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
EXAMPLE
2.1235229688575834915873..
MAPLE
Zeta(5/3) ; evalf(%) ;
PROG
(PARI) zeta(5/3)
KEYWORD
nonn,cons,new
AUTHOR
R. J. Mathar, Mar 19 2024
STATUS
approved
A371336 Decimal expansion of zeta(5/4). +0
0
4, 5, 9, 5, 1, 1, 1, 8, 2, 5, 8, 4, 2, 9, 4, 3, 3, 8, 0, 6, 8, 5, 3, 7, 8, 0, 3, 9, 6, 9, 4, 6, 2, 5, 6, 5, 2, 2, 8, 1, 0, 2, 9, 7, 8, 0, 6, 0, 4, 8, 0, 4, 8, 4, 6, 0, 2, 7, 1, 8, 9, 2, 7, 7, 9, 5, 5, 7, 9, 6, 0, 6, 0, 4, 0, 8, 0, 9, 0, 9, 6, 3, 3, 8, 1, 3, 4, 2, 6, 6, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
EXAMPLE
4.59511182584294338068537803..
MAPLE
Zeta(5/4) ; evalf(%) ;
KEYWORD
nonn,cons,new
AUTHOR
R. J. Mathar, Mar 19 2024
STATUS
approved
A371051 Ternary numbers consisting of a run of 1's, then a run of 2's, then a run of 0's. +0
0
120, 1120, 1200, 1220, 11120, 11200, 11220, 12000, 12200, 12220, 111120, 111200, 111220, 112000, 112200, 112220, 120000, 122000, 122200, 122220, 1111120, 1111200, 1111220, 1112000, 1112200, 1112220, 1120000, 1122000, 1122200, 1122220, 1200000, 1220000 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
MATHEMATICA
Map[#[[1]] &, Select[Map[{#, Map[#[[1]] &, Split[IntegerDigits[#, 3]]] == {1, 2, 0}} &,
Range[0, 4000, 3]], #[[2]] &]] (* A371050 *)
ToExpression[Map[IntegerString[#, 3] &, %]] (* this sequence *)
(* Peter J. C. Moses, Mar 06 2024 *)
CROSSREFS
KEYWORD
nonn,base,new
AUTHOR
Clark Kimberling, Mar 17 2024
STATUS
approved
A371050 Numbers whose ternary representation consists of a run of 1's, then a run of 2's, then a run of 0's. +0
0
15, 42, 45, 51, 123, 126, 132, 135, 153, 159, 366, 369, 375, 378, 396, 402, 405, 459, 477, 483, 1095, 1098, 1104, 1107, 1125, 1131, 1134, 1188, 1206, 1212, 1215, 1377, 1431, 1449, 1455, 3282, 3285, 3291, 3294, 3312, 3318, 3321, 3375, 3393, 3399, 3402, 3564 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All the numbers are multiples of 3.
LINKS
EXAMPLE
The ternary represerntations of 15, 42, 45 are 120, 1120, 1200.
MATHEMATICA
Map[#[[1]] &, Select[Map[{#, Map[#[[1]] &, Split[IntegerDigits[#, 3]]] == {1, 2, 0}} &,
Range[0, 4000, 3]], #[[2]] &]] (* this sequence *)
Map[IntegerString[#, 3] &, %] (* A371051 *)
(* Peter J. C. Moses, Mar 06 2024 *)
CROSSREFS
KEYWORD
nonn,base,new
AUTHOR
Clark Kimberling, Mar 17 2024
STATUS
approved
A371052 Numbers whose ternary representation consists of a run of 2's, then a run of 1's, then a run of 0's. +0
0
21, 63, 66, 75, 189, 198, 201, 225, 228, 237, 567, 594, 603, 606, 675, 684, 687, 711, 714, 723, 1701, 1782, 1809, 1818, 1821, 2025, 2052, 2061, 2064, 2133, 2142, 2145, 2169, 2172, 2181, 5103, 5346, 5427, 5454, 5463, 5466 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
All the numbers are multiples of 3.
LINKS
EXAMPLE
The ternary representations of 21, 63, 66 are 210, 2100, 2110.
MATHEMATICA
Map[#[[1]] &, Select[Map[{#, Map[#[[1]] &, Split[IntegerDigits[#, 3]]] == {2, 1, 0}} &,
Range[0, 6000, 3]], #[[2]] &]] (* this sequence *)
ToExpression[Map[IntegerString[#, 3] &, %]] (* A371053 *)
(* Peter J. C. Moses, Mar 06 2024 *)
CROSSREFS
KEYWORD
nonn,base,new
AUTHOR
Clark Kimberling, Mar 17 2024
STATUS
approved
A371281 Last digit of the product of decimal digits of n. +0
0
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 2, 4, 6, 8, 0, 2, 4, 6, 8, 0, 3, 6, 9, 2, 5, 8, 1, 4, 7, 0, 4, 8, 2, 6, 0, 4, 8, 2, 6, 0, 5, 0, 5, 0, 5, 0, 5, 0, 5, 0, 6, 2, 8, 4, 0, 6, 2, 8, 4, 0, 7, 4, 1, 8, 5, 2, 9, 6, 3, 0, 8, 6, 4, 2, 0, 8, 6, 4, 2, 0, 9, 8 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
n=0 is taken as one 0 digit so that its product of digits is A007954(0) = 0.
LINKS
FORMULA
a(n) = A007954(n) mod 10.
a(n) = A010879(A007954(n)).
EXAMPLE
n = 15: a(15) = 1*5 mod 10 = 5.
n = 26: a(26) = 2*6 mod 10 = 2.
MAPLE
a:= n-> `if`(n<10, n, irem(n, 10, 'q')*a(q) mod 10):
seq(a(n), n=0..92); # Alois P. Heinz, Mar 17 2024
MATHEMATICA
a[n_] := Mod[Times @@ IntegerDigits[n], 10]; Array[a, 100, 0] (* Amiram Eldar, Mar 17 2024 *)
PROG
(Python)
from math import prod
def a(n): return prod(map(int, str(n)))%10
print([a(n) for n in range(93)]) # Michael S. Branicky, Mar 17 2024
(PARI) a(n) = if (n==0, 0, vecprod(digits(n)) % 10); \\ Michel Marcus, Mar 17 2024
CROSSREFS
Cf. A007954, A010879, A036987 (similar for 2 instead of 10), A053837.
KEYWORD
nonn,base,new
AUTHOR
Ctibor O. Zizka, Mar 17 2024
STATUS
approved
page 1 2 3 4 5 6 7 8 9 10 ... 43

Search completed in 0.123 seconds

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 07:49 EDT 2024. Contains 370958 sequences. (Running on oeis4.)