A392135 - OEIS

%I #37 Jan 13 2026 13:40:20

%S 0,0,0,0,0,9,7,5,3,1,18,14,10,6,2,27,21,15,9,3,36,28,20,12,4,94,82,70,

%T 58,46,93,79,65,51,37,92,76,60,44,28,91,73,55,37,19,90,70,50,30,10,

%U 188,164,140,116,92,177,151,125,99,73,166,138,110,82,54,155,125

%N Third column of A391957.

%C Powers of 5 in the factorization of A391956.

%C The first 82 terms were obtained from a brute force calculation of A391956. From these results a regular pattern is observed to determine more terms.

%C See also A391957 for a Python program.

%H A.H.M. Smeets, <a href="/A392135/b392135.txt">Table of n, a(n) for n = 0..10000</a>

%F a(5^n) = 5*a(5^(n-1)) + 2*5^n - 1, a(1) = 0.

%F Conjectured: a(j*5^m + 5^(m-1)*k) = a(j*5^m) + k*(a(5^(m-1)) - 2*5^(m-1)*Sum_{i = 1..j} A055457(i)), 0 < k < 5, where a(j*5^m) = j*a(5^(m-1)) for j < 5.

%Y Cf. A055457, A391956, A391957.

%K nonn

%O 0,6

%A _A.H.M. Smeets_, Jan 01 2026