A072049 a(n) = floor(2^(n/(floor(n*log(2)/log(prime(n)))))).

2, 4, 8, 16, 32, 64, 128, 256, 512, 32, 45, 64, 90, 128, 181, 256, 362, 64, 80, 101, 128, 161, 203, 256, 322, 406, 107, 128, 152, 181, 215, 256, 304, 362, 430, 512, 168, 194, 222, 256, 294, 337, 388, 445, 512, 203, 228, 256, 287, 322, 362, 406, 456, 512, 574

Offset

1,1

Comments

The sequence comes from the relationship of the primes to powers of two: in Sierpiński gasket sets the number s(n)=log(prime(n))/log(2) is the Moran dimension of unique fractal types. I first thought of making numbers that take these to integers by multiplication. And then of using integers of those to make other integers as powers of two that were prime like.

The sequence is slow to increase and has an alternating effect so that it dips lower after reaching a peak.

Links

Table of n, a(n) for n=1..55.

Mathematica

Table[Floor[2^(n/(Floor[n * Log[2]/Log[Prime[n]]]))], {n, 60}]

Crossrefs

Sequence in context: A101440 A126605 A072067 * A281938 A242350 A115213

Adjacent sequences: A072046 A072047 A072048 * A072050 A072051 A072052

Keyword

nonn

Author

Roger L. Bagula, Jul 30 2002

Extensions

Edited by Robert G. Wilson v, Jul 31 2002

Status

approved