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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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 * A113305 A095078 A335874

Adjacent sequences:  A086078 A086079 A086080 * A086082 A086083 A086084

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified May 17 22:15 EDT 2021. Contains 343992 sequences. (Running on oeis4.)