A109496 a(n) is the first integer k for which b(b(...b(n)...))=5, where the transformation b(m), the m-th term of A008474, is taken k-1 times.

1, 4, 3, 2, 2, 3, 4, 3, 6, 5, 4, 5, 4, 3, 5, 4, 4, 5, 4, 3, 4, 5, 5, 4, 8, 7, 5, 4, 6, 5, 6, 3, 6, 5, 4, 5, 6, 5, 7, 6, 5, 6, 5, 4, 3, 4, 6, 4, 4, 3, 4, 7, 4, 7, 7, 6, 8, 7, 7, 3, 5, 6, 7, 6, 5, 5, 5, 4, 8, 7, 5, 4, 5, 5, 5, 4, 4, 6, 7, 6, 4, 6, 6, 5, 7, 6, 6, 5, 4, 7, 6, 5, 5, 4, 5, 5, 6, 5, 7, 6, 4, 5, 5, 4, 6

Offset

5,2

Links

Table of n, a(n) for n=5..109.

Example

a(6)=4 because b(6=2^1*3^1)=7, b(7=7^1)=8, b(8=2^3)=5, so we apply b(m) 3 times to get 5.

Mathematica

f[n_] := Sum[FactorInteger[n][[i]][[1]] + FactorInteger[n][[i]][[2]], { i, Length[FactorInteger[n]]}] g[t_, n_] := If[t == 1, n, f[g[t - 1, n]]]; a[n_] := Position[Array[g[ #, n] &, 100], 5, {1}, 1][[1, 1]]

Crossrefs

Cf. A008474.

Sequence in context: A171623 A117462 A155462 * A138851 A181061 A329934

Adjacent sequences: A109493 A109494 A109495 * A109497 A109498 A109499

Keyword

nonn

Author

Y. Kallus (yoav(AT)rice.edu), Aug 29 2005

Status

approved