

A152073


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


2



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
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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. 2919 = 10, not a power of 2. 2917 = 12, not a power of 2. But 2913 = 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(q1), nq==1<<valuation(nq, 2) && return(q)) \\ M. F. Hasler, Nov 23 2008


CROSSREFS

Cf. A065381, A139758, A152075, A152076, A156695.
Sequence in context: A242121 A242120 A259277 * A230606 A117289 A318719
Adjacent sequences: A152070 A152071 A152072 * A152074 A152075 A152076


KEYWORD

nonn,look,changed


AUTHOR

Leroy Quet, Nov 23 2008


EXTENSIONS

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


STATUS

approved



