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A152073
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a(n) = largest prime < p(n) such that p(n) - a(n) is a power of 2, where p(n) is the n-th prime; a(n) = 0 if no such prime exists.
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2
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2, 3, 5, 7, 11, 13, 17, 19, 13, 29, 29, 37, 41, 43, 37, 43, 59, 59, 67, 71, 71, 79, 73, 89, 97, 101, 103, 107, 109, 0, 127, 73, 137, 0, 149, 149, 131, 163, 157, 163, 179, 127, 191, 193, 197, 179, 191, 223, 227, 229, 223, 239, 0, 241, 199, 13, 269, 269, 277, 281, 277, 179
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| a(n) = 0 for odd primes p(n) appearing in A065381.
Primes p(n) for which there is no such prime a(n) (in which case a(n)=0) are listed in A065381 = (2,127,149,251,331,337,373,...). [From M. F. Hasler (www.univ-ag.fr/~mhasler), Nov 23 2008]
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EXAMPLE
| Looking at the primes less than the 10th prime = 29: 29 - 23 = 6, not a power of 2. 29-19 = 10, not a power of 2. 29-17 = 12, not a power of 2. But 29-13 = 16, a power of 2. Since p = 13 is the largest prime p such that 29 - p = a power of 2, then a(10) = 13.
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PROG
| (PARI) A152073(n)={ local( q=n=prime(n)); while( q=precprime(q-1), n-q==1<<valuation(n-q, 2) & return(q)) } [From M. F. Hasler (www.univ-ag.fr/~mhasler), Nov 23 2008]
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CROSSREFS
| Cf. A065381, A139758, A152075, A152076.
Sequence in context: A117094 A171057 A074721 * A117289 A106317 A152242
Adjacent sequences: A152070 A152071 A152072 * A152074 A152075 A152076
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Nov 23 2008
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EXTENSIONS
| Edited and extended by M. F. Hasler (www.univ-ag.fr/~mhasler) and Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 23 2008
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