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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.
3
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
OFFSET
0,1
COMMENTS
a(n) = A340117(n-1) for n >= 3.
LINKS
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
Sequence in context: A156387 A370065 A324040 * A361521 A223705 A358304
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Dec 28 2020
STATUS
approved