A379908 a(n) is number of n-digit positive integers in which the product of the digits in the even positions equals the product of the digits in the odd positions.

1, 9, 32, 380, 4097, 54054, 700099, 8742818, 108476326, 1285917070, 15207121743, 173726013062, 1982695287783, 22061642063204, 245374194718713, 2677923173095450, 29219674883924922, 314236528160399298, 3379020617685021774, 35924502411735093750, 381913758547904774763

Offset

1,2

Links

Table of n, a(n) for n=1..21.

Formula

Limit_{n->oo} a(n+1)/a(n) = 10.

Mathematica

a[n_]:=Module[{num=KroneckerDelta[n, 1]}, For[k=10^(n-1), k<=10^n-1, k++, If[Product[Part[(digits=IntegerDigits[k]), 2i], {i, Floor[(len=IntegerLength[k])/2]}] == Product[Part[digits, 2i-1], {i, Ceiling[len/2]}], num++]]; num]; Array[a, 6]

Crossrefs

Cf. A067042.

Sequence in context: A196016 A183426 A061913 * A264512 A231764 A208136

Adjacent sequences: A379904 A379906 A379907 * A379909 A379910 A379911

Keyword

nonn,base,new

Author

Stefano Spezia, Jan 05 2025

Extensions

More terms from Jinyuan Wang, Jan 07 2025

Status

approved