A185337 - OEIS

A185337

Primes p(n) such that p(n) < 2^((p(n+1) - p(n))/2).

113, 887, 1129, 1327, 1669, 1951, 2179, 2477, 2971, 3137, 3271, 4297, 4831, 5119, 5351, 5531, 5591, 5749, 5953, 6491, 6917, 7253, 7759, 7963, 8389, 8467, 8893, 8971, 9551, 9973, 10009, 10399, 10531, 10799, 10909, 11551, 11743, 12163, 12853, 13063, 13187

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

EXAMPLE

113 is in the sequence because prime(30) < 2^((prime(30+1)-prime(30))/2) or 113 < 2^((127-113)/2).

MATHEMATICA

Select[Prime[Range[2000]], # < 2^((NextPrime[#] - #)/2) &] (* T. D. Noe, Mar 07 2012 *)

PROG

(PARI) v=List(); p=2; forprime(q=3, 1e4, if(p<2^((q-p)/2), listput(v, p)); p=q); Vec(v) \\ Charles R Greathouse IV, Aug 03 2012

CROSSREFS