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
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
Programs
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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
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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