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Search: id:A086081
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| A086081 |
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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. |
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3
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| 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; listen)
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OFFSET
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1,1
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COMMENT
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In the first 672509 primes, 64894 of them (about 9.65%) are 2's-complement primes.
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FORMULA
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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 (shevelev(AT)bgu.ac.il), Dec 04 2008]
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EXAMPLE
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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.
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CROSSREFS
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Cf. A068811.
Sequence in context: A109640 A105961 A045361 this_sequence A113305 A095078 A062572
Adjacent sequences: A086078 A086079 A086080 this_sequence A086082 A086083 A086084
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KEYWORD
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nonn
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AUTHOR
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Chuck Seggelin (barkeep(AT)plastereddragon.com), Jul 08 2003
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