A381492 a(n) is the logarithm to base A381491(n) of A381487(n).

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 7, 4, 3, 3, 4, 4, 13, 7, 5, 5, 7, 19, 6, 7, 10, 7, 7, 25, 8, 13, 9, 10, 9, 13, 31, 10, 16, 11, 11, 13, 37, 19, 12, 13, 13, 43, 22, 19, 14, 16, 15, 15, 49, 25, 16, 17, 19, 17, 55, 28, 19, 18, 25, 19, 61, 22, 31, 21, 20, 21, 67, 34, 23, 22, 25

Offset: 1

Author

Stefano Spezia, Feb 25 2025

Keywords

• nonn
• base

Examples

			a(12) = 7 since A381487(12) = 128 = 2^7 = A381491(12)^a(12).
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..3347

Crossrefs

Cf. A381487, A381491.

Programs

Mathematica

A010888[n_]:=n - 9*Floor[(n-1)/9]; kmax=5*10^6; a={0,1}; For[k=2, k<=kmax, k++, If[A010888[k]!=1, If[IntegerQ[e=Log[A010888[k],k]], AppendTo[a,e]]]]; a

PARI

dr(n) = if(n, (n-1)%9+1); \\ A010888
expo(n, k) = if (n<=1, n, logint(n, k));
lista(nn) = my(list = List()); listput(list, 0); listput(list, 1); for (n=2, 9, for (k=1, logint(nn, n), if (dr(n^k) == n, listput(list, n^k)););); my(w=vecsort(Vec(list)), ws=apply(x->dr(x), w)); vector(#w, k, expo(w[k], ws[k])); \\ Michel Marcus, Feb 27 2025

Extensions

More terms from Michel Marcus, Feb 27 2025