A086081 Numbers n such that n and its 2's complement are both primes. In other words, n and 2^k - n (where k is the smallest power of 2 such that 2^k > n) are primes.

2, 5, 11, 13, 19, 29, 41, 47, 53, 59, 61, 67, 97, 109, 149, 167, 173, 197, 227, 233, 239, 251, 271, 283, 313, 331, 349, 373, 409, 433, 439, 499, 509, 521, 557, 563, 593, 641, 677, 743, 761, 773, 797, 827, 857, 887, 911, 941, 953, 971, 977, 983, 1013, 1019, 1021

Offset

1,1

Comments

In the first 672509 primes, 64894 of them (about 9.65%) are 2's-complement primes.

Links

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

Formula

If isPrime(p) And isPrime(2^(floor(Log(p, 2)) + 1) - p) then sequence.add(p)

If A(x) is the counting function of the terms a(n) <= x, then A(x) = O(xloglogx/(logx)^2) [From Vladimir Shevelev, Dec 04 2008]

Example

a(5) = 19 because 19 is prime and (2^5 - 19) = (32 - 19) = 13 which is prime.
a(74) = 1777 because 1777 is prime and (2^11 - 1777) = (2048 - 1777) = 271 which is prime.

Mathematica

Join[{2}, Select[Prime[Range[250]], PrimeQ[BitXor[#, 2^Ceiling[Log[2, #]] - 1] + 1] &]] (* Alonso del Arte, Feb 12 2013 *)

Prog

(PARI) select(n->isprime((2<<(log(n+.5)\log(2)))-n), primes(100)) \\ Charles R Greathouse IV, Feb 13 2013

Crossrefs

Cf. A068811.

Sequence in context: A105961 A045361 A276660 * A345707 A113305 A095078

Adjacent sequences: A086078 A086079 A086080 * A086082 A086083 A086084

Keyword

nonn,easy

Author

Chuck Seggelin (barkeep(AT)plastereddragon.com), Jul 08 2003

Status

approved