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 A072049 a(n) = floor(2^(n/(floor(n*log(2)/log(prime(n)))))). 1

%I

%S 2,4,8,16,32,64,128,256,512,32,45,64,90,128,181,256,362,64,80,101,128,

%T 161,203,256,322,406,107,128,152,181,215,256,304,362,430,512,168,194,

%U 222,256,294,337,388,445,512,203,228,256,287,322,362,406,456,512,574

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

%C The sequence comes from the relationship of the primes to powers of two: in SierpiĆski 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.

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

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

%K nonn

%O 1,1

%A _Roger L. Bagula_, Jul 30 2002

%E Edited by _Robert G. Wilson v_, Jul 31 2002

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Last modified June 16 19:49 EDT 2021. Contains 345068 sequences. (Running on oeis4.)