A309954 -id:A309954 - 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)).

A355487 Bitwise XOR of the base-4 digits of n.

Original entry on oeis.org

0, 1, 2, 3, 1, 0, 3, 2, 2, 3, 0, 1, 3, 2, 1, 0, 1, 0, 3, 2, 0, 1, 2, 3, 3, 2, 1, 0, 2, 3, 0, 1, 2, 3, 0, 1, 3, 2, 1, 0, 0, 1, 2, 3, 1, 0, 3, 2, 3, 2, 1, 0, 2, 3, 0, 1, 1, 0, 3, 2, 0, 1, 2, 3, 1, 0, 3, 2, 0, 1, 2, 3, 3, 2, 1, 0, 2, 3, 0, 1, 0, 1, 2, 3, 1, 0, 3

Offset: 0

Kevin Ryde, Jul 04 2022

Equivalently, the parity of the odd position 1-bits of n and the parity of the even position 1-bits of n, combined as a(n) = 2*A269723(n) + A341389(n).

In GF(2)[x] polynomials encoded as bits of an integer (least significant bit for the constant term), a(n) is remainder n mod x^2 + 1.

			n=35 has base-4 digits 203 so a(35) = 2 XOR 0 XOR 3 = 1.

Cf. A030373 (base 4 digits), A003987 (XOR).
Cf. A341389, A269723, A010060.
Cf. A353167 (indices of 0's).
Other digit operations: A053737 (sum), A309954 (product).

a[n_] := BitXor @@ IntegerDigits[n, 4]; Array[a, 100, 0] (* Amiram Eldar, Jul 05 2022 *)

a(n) = if(n==0,0, fold(bitxor,digits(n,4)));

from operator import xor
from functools import reduce
from sympy.ntheory import digits
def a(n): return reduce(xor, digits(n, 4)[1:])
print([a(n) for n in range(87)]) # Michael S. Branicky, Jul 05 2022

Fixed point of the morphism 0 -> 0,1; 1 -> 2,3; 2 -> 1,0; 3 -> 3,2 starting from 0.

A338854 Product of the nonzero digits of (n written in base 4).

Original entry on oeis.org

1, 1, 2, 3, 1, 1, 2, 3, 2, 2, 4, 6, 3, 3, 6, 9, 1, 1, 2, 3, 1, 1, 2, 3, 2, 2, 4, 6, 3, 3, 6, 9, 2, 2, 4, 6, 2, 2, 4, 6, 4, 4, 8, 12, 6, 6, 12, 18, 3, 3, 6, 9, 3, 3, 6, 9, 6, 6, 12, 18, 9, 9, 18, 27, 1, 1, 2, 3, 1, 1, 2, 3, 2, 2, 4, 6, 3, 3, 6, 9, 1

Offset: 0

Ilya Gutkovskiy, Nov 12 2020

Cf. A007090, A051801, A117592, A160382, A160383, A309954.

Table[Times @@ DeleteCases[IntegerDigits[n, 4], 0], {n, 0, 80}]
nmax = 80; A[] = 1; Do[A[x] = (1 + x + 2 x^2 + 3 x^3) A[x^4] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

a(n) = vecprod(select(x->x, digits(n, 4))); \\ Michel Marcus, Nov 12 2020

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

a(n) = 2^A160382(n) * 3^A160383(n).

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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A355487 Bitwise XOR of the base-4 digits of n.

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A338854 Product of the nonzero digits of (n written in base 4).

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