A267091 Primes p such that p*(2^k)+1 is also prime, where 2^k is the largest power of 2 smaller than p.

2, 3, 7, 11, 53, 59, 67, 73, 109, 149, 167, 239, 277, 307, 331, 421, 433, 457, 463, 487, 563, 593, 599, 683, 719, 743, 809, 821, 929, 971, 983, 1013, 1069, 1087, 1117, 1129, 1303, 1399, 1453, 1567, 1579, 1597, 1609, 1987, 2087, 2111, 2129, 2141, 2267, 2339, 2477

Offset

1,1

Comments

The corresponding primes are 3, 7, 29, 89, 1697, 1889, 4289, 4673, 6977, 19073, 21377, 30593, 70913, 78593, 84737, 107777, 110849, 116993, 118529, 124673, 288257, 303617, 306689, 349697, 368129, 380417, 414209, 420353, 475649, 497153, 503297, ...

Links

Table of n, a(n) for n=1..51.

Example

3*(2^1)+1=7(is prime) => p=3, (2^k)=2; (2^k)<p; 2<3.
11*(2^3)+1=89(is prime) => p=11, (2^k)=8; (2^k)<p; 8<11.
73*(2^6)+1=4673(is prime) => p=73, (2^k)=64; (2^k)<p; 64<73.

Mathematica

Select[Prime@ Range@ 400, PrimeQ[# 2^IntegerPart@ Log2@ # + 1] &] (* Michael De Vlieger, Jan 11 2016 *)

Crossrefs

Sequence in context: A106125 A175171 A073609 * A053781 A066749 A306786

Adjacent sequences: A267088 A267089 A267090 * A267092 A267093 A267094

Keyword

nonn

Author

Emre APARI, Jan 10 2016

Status

approved