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a(n) = smallest m such that m+2^j and m-2^j are prime for all 0 < j <= n.
4

%I #12 Aug 17 2020 01:58:31

%S 5,9,15,50943795,40874929095,616517522595975,93487500801880185,

%T 64606701602327559675

%N a(n) = smallest m such that m+2^j and m-2^j are prime for all 0 < j <= n.

%C Is this sequence infinite?

%H Felice Russo, <a href="http://www.primepuzzles.net/puzzles/puzz_167.htm">Prime puzzle 167</a>.

%H Marek Wolf, <a href="https://pdfs.semanticscholar.org/78a1/7349819304863ae061df88dbcb26b4908f03.pdf">Conjectures on the gaps between consecutive primes</a>

%e 9-4, 9-2, 9+2, 9+4 are prime, but not 5+4 = 7+2, therefore a(2) = 9.

%Y Prime quadruples: A014561, sextets: A061671, octets: A066082.

%K hard,nonn

%O 1,1

%A _Frank Ellermann_, Dec 03 2001

%E a(5) and a(6) from _Don Reble_, Dec 07 2001

%E a(7) from Jim Fougeron (Feb 07) confirmed by Phil Carmody, who also found a(8) (Feb 14 2002).