A356859 -id:A356859 - cp's OEIS frontend

A356858 a(n) is the product of the first n numbers not divisible by 5.

1, 1, 2, 6, 24, 144, 1008, 8064, 72576, 798336, 9580032, 124540416, 1743565824, 27897053184, 474249904128, 8536498274304, 162193467211776, 3406062811447296, 74933381851840512, 1723467782592331776, 41363226782215962624, 1075443896337615028224, 29036985201115605762048

Offset: 0

Stefano Spezia, Sep 01 2022

nonn

Unlike the factorial number n!, a(n) does not have trailing zeros.

Harvey P. Dale, Table of n, a(n) for n = 0..434

Cf. A000142, A000351, A002266, A047201.

Cf. A356859 (number of zero digits), A356860 (number of digits), A356861 (number of nonzero digits).

Table[Product[Floor[(5k-1)/4], {k,n}], {n,0,22}] (* or *)
Join[{1}, Table[Floor[(5n-1)/4]!/(Floor[Floor[(5n-1)/4]/5]!*5^Floor[Floor[(5n-1)/4]/5]), {n,22}]]
Join[{1},FoldList[Times,Table[If[Mod[n,5]==0,Nothing,n],{n,30}]]] (* Harvey P. Dale, Nov 03 2024 *)

from math import prod
def a(n): return prod((5*k-1)//4 for k in range(1, n+1))
print([a(n) for n in range(23)]) # Michael S. Branicky, Sep 01 2022

a(n) = Product_{k=1..n} A047201(k).

a(n) = A047201(n)!/(floor(A047201(n)/5)!*5^floor(A047201(n)/5)) for n > 0.

A356860 a(n) is the number of digits in the product of the first n numbers not divisible by 5.

Original entry on oeis.org

1, 1, 1, 1, 2, 3, 4, 4, 5, 6, 7, 9, 10, 11, 12, 13, 15, 16, 17, 19, 20, 22, 23, 24, 26, 27, 29, 30, 32, 33, 35, 37, 38, 40, 41, 43, 45, 46, 48, 50, 51, 53, 55, 57, 58, 60, 62, 64, 65, 67, 69, 71, 73, 74, 76, 78, 80, 82, 84, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103

Offset: 0

Stefano Spezia, Sep 01 2022

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Cf. A047201, A055642, A356858.

Cf. A356859 (number of zero digits), A356861 (number of nonzero digits).

Table[Length[IntegerDigits[Product[Floor[(5i-1)/4], {i,n}]]], {n,0,68}]
Join[{1},IntegerLength/@FoldList[Times,Table[If[Mod[n,5]==0,Nothing,n],{n,0,100}]]] (* Harvey P. Dale, Jul 20 2025 *)

from math import prod
def a(n): return len(str(prod((5*k-1)//4 for k in range(1, n+1))))
print([a(n) for n in range(69)]) # Michael S. Branicky, Sep 01 2022

a(n) = A055642(A356858(n)).

A356861 a(n) is the number of nonzero digits in the product of the first n numbers not divisible by 5.

Original entry on oeis.org

1, 1, 1, 1, 2, 3, 2, 3, 5, 6, 5, 8, 10, 10, 11, 12, 15, 14, 16, 19, 20, 20, 19, 23, 24, 25, 27, 24, 27, 31, 32, 32, 34, 38, 36, 40, 41, 40, 44, 47, 43, 50, 52, 53, 50, 51, 56, 61, 60, 58, 63, 61, 64, 67, 72, 67, 70, 72, 76, 72, 78, 84, 83, 85, 84, 90, 91, 91, 90

Offset: 0

Stefano Spezia, Sep 01 2022

Cf. A047201, A055640, A356858.

Cf. A356859 (number of zero digits), A356860 (number of digits).

Table[Length[Select[IntegerDigits[Product[Floor[(5i-1)/4], {i,n}]], Positive]], {n,0,68}]

from math import prod
def a(n): s = str(prod((5*k-1)//4 for k in range(1, n+1))); return len(s) - s.count("0")
print([a(n) for n in range(69)]) # Michael S. Branicky, Sep 01 2022

a(n) = A055640(A356858(n)).

A358991 a(n) is the number of zero digits in the product of the first n odd numbers not divisible by 5.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 2, 1, 0, 2, 1, 1, 2, 2, 3, 2, 2, 2, 3, 2, 4, 5, 2, 4, 1, 3, 4, 5, 6, 9, 5, 4, 6, 4, 7, 7, 10, 5, 7, 10, 8, 9, 8, 4, 7, 4, 15, 9, 4, 7, 12, 9, 8, 14, 12, 5, 14, 12, 6, 11, 10, 14, 17, 17, 11, 19, 11, 15, 19, 15, 13, 14, 11, 19

Offset: 0

Stefano Spezia, Dec 09 2022

Cf. A045572, A055641, A356859, A358990.

Cf. A358992 (number of digits), A358993 (number of nonzero digits).

Table[Count[IntegerDigits[Product[2i+2Floor[(i-3)/4]+1, {i, n}]], 0], {n, 0, 80}]

a(n) = A055641(A356990(n)).

cp's OEIS Frontend

A356858 a(n) is the product of the first n numbers not divisible by 5.

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A356860 a(n) is the number of digits in the product of the first n numbers not divisible by 5.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Python

Formula

A356861 a(n) is the number of nonzero digits in the product of the first n numbers not divisible by 5.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Python

Formula

A358991 a(n) is the number of zero digits in the product of the first n odd numbers not divisible by 5.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

Formula