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a(n) = (q^2 - A340116(n)^2)/2^n where q is the next prime after A340116(n).
1

%I #11 Jul 26 2022 10:09:56

%S 5,2,1,3,1,21,45,15,3,9,105,39,63,105,3,75,57,99,273,69,3,231,15,315,

%T 33,495,603,39,1617,975,63,285,1995,171,765,141,603,429,1677,339,2793,

%U 231,273,315,435,9,765,69,4257,735,1485,1245,423,585,375,1155,333,645,105,231,1965,1209,63,735

%N a(n) = (q^2 - A340116(n)^2)/2^n where q is the next prime after A340116(n).

%H Robert Israel, <a href="/A350688/b350688.txt">Table of n, a(n) for n = 0..1000</a>

%e A340116(5) = 53 and the next prime is 59, so a(5) = (59^2 - 53^2)/2^5 = 21.

%Y Cf. A340116.

%K nonn

%O 0,1

%A _J. M. Bergot_ and _Robert Israel_, Jan 11 2022