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.
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
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Dec 28 2020
STATUS
approved