A152073 a(n) = largest prime < prime(n) such that prime(n) - a(n) is a power of 2, where prime(n) is the n-th prime; a(n) = 0 if no such prime exists.

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

Offset

2,1

Comments

a(n) = 0 for odd primes prime(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,...). - M. F. Hasler, Nov 23 2008

Links

Ivan Neretin, Table of n, a(n) for n = 2..10000

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.

Mathematica

Table[Max[0, Select[# - 2^Range[0, Log2@#] &@Prime[n], PrimeQ]], {n, 2, 63}] (* Ivan Neretin, Jun 10 2018 *)

Prog

(PARI) A152073(n)=local( q=n=prime(n)); while( q=precprime(q-1), n-q==1<<valuation(n-q, 2) && return(q)) \\ M. F. Hasler, Nov 23 2008

Crossrefs

Cf. A065381, A139758, A152075, A152076, A156695.

Sequence in context: A242121 A242120 A259277 * A331046 A329150 A230606

Adjacent sequences: A152070 A152071 A152072 * A152074 A152075 A152076

Keyword

nonn,look

Author

Leroy Quet, Nov 23 2008

Extensions

Edited and extended by M. F. Hasler and Ray Chandler, Nov 23 2008

Status

approved