A152084 Primes p such that p + 2^floor(log_2(p)) is prime.

3, 7, 11, 31, 41, 47, 67, 73, 103, 109, 127, 149, 179, 239, 251, 307, 313, 331, 337, 397, 421, 463, 487, 521, 557, 617, 641, 659, 701, 719, 809, 887, 911, 941, 947, 971, 977, 1019, 1039, 1063, 1087, 1117, 1129, 1213, 1249, 1327, 1399, 1423, 1453, 1567, 1597

Offset: 1

Author

Leroy Quet, Nov 23 2008

Keywords

• nonn

Comments

a(n) + 2^floor(log_2(a(n))) = A152085(n).

If a(n) is written in binary and the leftmost 1 is replaced with "10", then we would have the binary representation of A152085(n), which is a prime.

Sequence A091932 contains the related primes p where p - 2^floor(log_2(p)) = prime.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

A152085, A091932

Programs

Maple

filter:= n -> isprime(n) and isprime(n + 2^ilog2(n)):
select(filter, [seq(i,i=3..10000,2)]); # Robert Israel, Mar 14 2024

Extensions

Extended by Ray Chandler, Nov 26 2008