A309953 -id:A309953 - cp's OEIS frontend

A309788 Product of digits of (n written in base 9).

0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 2, 4, 6, 8, 10, 12, 14, 16, 0, 3, 6, 9, 12, 15, 18, 21, 24, 0, 4, 8, 12, 16, 20, 24, 28, 32, 0, 5, 10, 15, 20, 25, 30, 35, 40, 0, 6, 12, 18, 24, 30, 36, 42, 48, 0, 7, 14, 21, 28, 35, 42, 49, 56, 0, 8, 16, 24, 32, 40, 48, 56, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 2

Offset: 0

Ilya Gutkovskiy, Aug 26 2019

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Product of digits of (n written in base k): A309953 (k = 3), A309954 (k = 4), A309956 (k = 5), A309957 (k = 6), A309958 (k = 7), A309959 (k = 8), this sequence (k = 9), A007954 (k = 10).

Cf. A007095, A053830.

[0] cat [&*Intseq(n,9):n in [1..100]]; // Marius A. Burtea, Aug 26 2019

Table[Times @@ IntegerDigits[n, 9], {n, 0, 100}]

G.f. A(x) satisfies: A(x) = x * (1 + 2*x + 3*x^2 + 4*x^3 + 5*x^4 + 6*x^5 + 7*x^6 + 8*x^7) * (1 + A(x^9)).

A309958 Product of digits of (n written in base 7).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 0, 1, 2, 3, 4, 5, 6, 0, 2, 4, 6, 8, 10, 12, 0, 3, 6, 9, 12, 15, 18, 0, 4, 8, 12, 16, 20, 24, 0, 5, 10, 15, 20, 25, 30, 0, 6, 12, 18, 24, 30, 36, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 0, 2, 4, 6, 8, 10, 12, 0, 3, 6, 9, 12, 15, 18, 0, 4, 8, 12, 16, 20, 24, 0, 5, 10, 15, 20, 25, 30, 0, 6, 12, 18, 24, 30, 36, 0, 0, 0

Offset: 0

Ilya Gutkovskiy, Aug 24 2019

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Product of digits of (n written in base k): A309953 (k = 3), A309954 (k = 4), A309956 (k = 5), A309957 (k = 6), this sequence (k = 7), A309959 (k = 8), A309788 (k = 9), A007954 (k = 10).

Cf. A007093, A053828.

[0] cat [&*Intseq(n,7):n in [1..100]]; // Marius A. Burtea, Aug 25 2019

Table[Times @@ IntegerDigits[n, 7], {n, 0, 100}]

a(n) = my(v=vecprod(digits(n, 7))); n>0 && return(v) \\ Felix Fröhlich, Sep 09 2019

G.f. A(x) satisfies: A(x) = x * (1 + 2*x + 3*x^2 + 4*x^3 + 5*x^4 + 6*x^5) * (1 + A(x^7)).

A309959 Product of digits of (n written in base 8).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 2, 3, 4, 5, 6, 7, 0, 2, 4, 6, 8, 10, 12, 14, 0, 3, 6, 9, 12, 15, 18, 21, 0, 4, 8, 12, 16, 20, 24, 28, 0, 5, 10, 15, 20, 25, 30, 35, 0, 6, 12, 18, 24, 30, 36, 42, 0, 7, 14, 21, 28, 35, 42, 49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 0, 2, 4, 6, 8, 10, 12, 14, 0, 3, 6, 9, 12, 15, 18, 21, 0, 4, 8, 12, 16

Offset: 0

Ilya Gutkovskiy, Aug 24 2019

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Product of digits of (n written in base k): A309953 (k = 3), A309954 (k = 4), A309956 (k = 5), A309957 (k = 6), A309958 (k = 7), this sequence (k = 8), A309788 (k = 9), A007954 (k = 10).

Cf. A007094, A053829.

[0] cat [&*Intseq(n,8):n in [1..100]]; // Marius A. Burtea, Aug 25 2019

Table[Times @@ IntegerDigits[n, 8], {n, 0, 100}]

G.f. A(x) satisfies: A(x) = x * (1 + 2*x + 3*x^2 + 4*x^3 + 5*x^4 + 6*x^5 + 7*x^6) * (1 + A(x^8)).

A371222 Product of digits of (n written in base 3) mod 3.

Original entry on oeis.org

0, 1, 2, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 0

Ctibor O. Zizka, Mar 18 2024

a(A032924(n)) = 1 or 2. For n >= 1, a(A032924(n)) - 1 = A309953(A032924(n)) mod 3 - 1 = A010059(n+1).

			n = 5: 5_10 = 12_3 thus a(5) = 1*2 mod 3 = 2.
n = 8: 8_10 = 22_3 thus a(8) = 2*2 mod 3 = 1.

Cf. A007089, A010059, A032924, A081605, A309953, A371281 (base 10).

a[n_] := Mod[Times @@ IntegerDigits[n, 3], 3]; Array[a, 100, 0] (* Amiram Eldar, Mar 18 2024 *)

from functools import reduce
from sympy.ntheory import digits
def A371222(n): return reduce(lambda a,b: a*b%3,digits(n,3)[1:],1) # Chai Wah Wu, Mar 19 2024

a(n) = A309953(n) mod 3.

a(A081605(n)) = 0.

cp's OEIS Frontend

A309788 Product of digits of (n written in base 9).

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A309958 Product of digits of (n written in base 7).

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A309959 Product of digits of (n written in base 8).

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A371222 Product of digits of (n written in base 3) mod 3.

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