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A209611
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Primes p(n) such that p(n)*(p(n+1)-p(n)) <= 2^(p(n+1)-p(n)).
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0
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2, 113, 199, 211, 293, 317, 523, 773, 839, 863, 887, 953, 1069, 1129, 1259, 1327, 1381, 1637, 1669, 1759, 1831, 1913, 1933, 1951, 2113, 2161, 2179, 2221, 2251, 2311, 2477, 2503, 2557, 2593, 2803, 2861, 2971, 3089, 3121, 3137, 3229, 3271, 3373, 3391, 3413, 3433
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OFFSET
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1,1
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COMMENTS
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Primes prime(n) which multiplied by the associated prime gap g=A001223(n) remain <= 2^g.
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LINKS
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EXAMPLE
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2 is in the sequence because 2*(3-2) = 2^(3-2), 113 is in the sequence because 113*(127-113) < 2^(127-113).
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PROG
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(PARI) isA209611(p)={
local(q=nextprime(p+1)-p) ;
return(isprime(p) && p*q <= 2^q) ; }
{
forprime(p=2, 3100, if(isA209611(p), print1(p" ") ) ; ) ;
} /* R. J. Mathar, Mar 19 2012 */
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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