A089996 a(n) = primes generated by the function ( f[n_]=Floor[(A004001[n]*Prime[n])*Log[2]/(2*PrimePi[n]+1)]).

3, 5, 13, 17, 41, 53, 59, 61, 101, 127, 151, 167, 193, 269, 277, 281, 283, 313, 359, 419, 421, 439, 463, 467, 499, 509, 619, 691, 743, 787, 853, 859, 907, 1061, 1069, 1097, 1181, 1229, 1249, 1277, 1289, 1303, 1381, 1427, 1453, 1531, 1571, 1583, 1609, 1741

Offset: 1

Author

Roger L. Bagula, Jan 14 2004

Keywords

• nonn

Comments

A prime generating function based on the primes, A004001 and the distribution of the primes.

By itself the integer function : f[n_]=Floor[(Conway[n]*Prime[n])*Log[2]/(2*PrimePi[n]+1)] is not very interesting: it is made to match the function g[n_]=n*Log[n]

Crossrefs

Cf. A004001.

Programs

Mathematica

digits=6*200 Conway[n_Integer?Positive] := Conway[n] =Conway[Conway[n-1]] + Conway[n - Conway[n-1]] Conway[1] = Conway[2] = 1 (* PrimeQ sieve function *) a=Table[If[PrimeQ[Floor[(Conway[n]*Prime[n])*Log[2]/(2*PrimePi[n]+1)]]==True, Floor[(Conway[n]*Prime[n])*Log[2]/(2*PrimePi[n]+1)], 0], {n, 1, digits}] (* eliminate the extra zeros *) b=Union[a] Delete[b, 1]