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 A340116 a(n) is the least prime p such that the 2-adic valuation of q^2-p^2 is n, where q is the next prime after p, or 0 if there is no such p. 2
 2, 0, 0, 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) = A340117(n-1) for n >= 3. LINKS Robert Israel, Table of n, a(n) for n = 0..1000 EXAMPLE a(3) = 5 because 5 is prime, the next prime is 7, 7^2-5^2 = 24 = 2^3*3, and this is the first prime p in which 2^3 appears in the factorization of q^2-p^2. MAPLE g:= proc(m) local k, p;   for k from 2^(m-2) by 2^(m-1) do     p:= prevprime(k);     if nextprime(p) = 2*k-p then return p fi   od end proc: g(0):= 2: g(1):= 0: g(2):= 0: g(3):= 5: map(g, [\$0..30]); CROSSREFS Cf. A007814 Sequence in context: A143160 A156387 A324040 * A223705 A285192 A278177 Adjacent sequences:  A340113 A340114 A340115 * A340117 A340118 A340119 KEYWORD nonn AUTHOR J. M. Bergot and Robert Israel, Dec 28 2020 STATUS approved

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Last modified August 5 06:37 EDT 2021. Contains 346458 sequences. (Running on oeis4.)