A088660 A logarithmic scale Sierpinski self-similar sequence.

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

Offset: 3

Author

Roger L. Bagula, Nov 21 2003

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 3..5000

Crossrefs

Cf. A088487 (self-similar Sierpinski type chaotic sequence with rate three at eight levels), A088488 (self-similar Cantor type sequence with eight levels).

Programs

Mathematica

p[n_, k_]:= Sum[Log[i], {i, 1, n}]/Sum[Log[i], {i, 1, n-Floor[n/2^k]}]; f[n_]=Sum[Floor[p[n, k]/p[n-1, k]], {k, 1, 8}]; Table[f[n], {n, 3, 100}]

Formula

With p(n, k) = log(n!) / log((n-floor(n/2^k))!) then a(n) = Sum_{k=1..8} floor(p(n, k)/p(n-1, k)) for n>2.