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

Author

Stefano Spezia, Jan 05 2025

Keywords

• nonn
• base

Crossrefs

Cf. A067042.

Programs

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]

Formula

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

Extensions

More terms from Jinyuan Wang, Jan 07 2025