A340117 a(n) is the least prime p such that the 2-adic valuation of p+q is n, where q is the next prime after p, or 0 if there is no such p.

2, 7, 5, 3, 53, 139, 157, 61, 1151, 3833, 6653, 7159, 30713, 4093, 204797, 311293, 360439, 2555897, 3014653, 786431, 11010037, 5242877, 73400311, 138412031, 461373431, 1124073463, 436207613, 3288334303, 10066329587, 1879048183, 8053063661, 102005473259, 40802189303, 193273528303, 403726925821

Offset

0,1

Comments

a(n)=A340116(n+1) for all n >= 2.

Dickson's conjecture implies that a(n) always exists, as for any n there will be k such that p = 2^(n-1)-1+k*2^n and q = p+2 = 2^(n-1)+1+k*2^n are primes.

Links

Table of n, a(n) for n=0..34.

Example

a(4) = 53 because 53 is prime, the next prime is 59, 53+59 = 112 = 2^4*7, and this is the first prime p in which 2^4 appears in the factorization of p+q.

Maple

g:= proc(m) local k, p;
  for k from 2^(m-1) by 2^m do
    p:= prevprime(k);
    if nextprime(p) = 2*k-p then return p fi
  od
end proc:
g(0):= 2: g(1):= 7: g(2):= 5:map(g, [$0..30]);

Crossrefs

Cf. A007814, A340116.

Sequence in context: A354633 A171037 A246205 * A160669 A301816 A021367

Adjacent sequences: A340114 A340115 A340116 * A340118 A340119 A340120

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Dec 28 2020

Status

approved