

A153352


Kbit primes p such that p2^i and p+2^i are composite for 0<=i<=K1.


5



1973, 3181, 3967, 4889, 8363, 8923, 11437, 12517, 14489, 19583, 19819, 21683, 21701, 21893, 22147, 22817, 24943, 27197, 27437, 28057, 29101, 34171, 34537, 34919, 35201, 35437, 36151, 38873, 41947, 42169, 42533, 42943, 43103, 43759
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Sun showed that the sequence is of positive density in the primes; in particular, of relative density >= 7.9 * 10^29 = 1/phi(66483034025018711639862527490).
Terry Tao gives this sequence explicitly (p. 1) and generalizes Sun's result.


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Fred Cohen and J. L. Selfridge, Not every number is the sum or difference of two prime powers, Math. Comput. 29 (1975), pp. 7981.
ZhiWei Sun, On integers not of the form +p^a + q^b, Proceedings of the American Mathematical Society 128:4 (2000), pp. 9971002.
Terence Tao, A remark on primality testing and decimal expansions, Journal of the Australian Mathematical Society 91:3 (2011), pp. 405413.
Terence Tao, A remark on primality testing and the binary expansion (blog entry)


EXAMPLE

a(1)=1973 because 1973 has 11 bits, and 1973 +1, 1973 +2, 1973 +4, 1973 +8, 1973 +16, 1973 +32, 1973 +64, 1973 +128, 1973 +256, 1973 +512, and 1973 +2^10 are all composite.


PROG

(PARI)f(p)={v=binary(p); k=#v; for(i=0, k1, if(isprime(p+2^i)isprime(p2^i), return(0))); return(1)}; forprime(p=2, 43759, if(f(p), print1(p, ", "))) \\ Washington Bomfim, Jan 18 2011


CROSSREFS

Cf. A065092.
Subsequence of A255967.
Sequence in context: A183692 A206218 A255967 * A251816 A108386 A135844
Adjacent sequences: A153349 A153350 A153351 * A153353 A153354 A153355


KEYWORD

nonn,base


AUTHOR

Charles R Greathouse IV, Dec 24 2008


EXTENSIONS

Edited by Washington Bomfim, Jan 18 2011


STATUS

approved



