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 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. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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 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: A138344 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

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Last modified August 2 21:30 EDT 2021. Contains 346429 sequences. (Running on oeis4.)