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%I #8 Aug 04 2021 14:25:13
%S 0,2,2,3,4,2,3,4,8,6,2,3,4,10,6,7,8,2,3,4,17,6,7,8,21,10,2,3,4,21,6,7,
%T 8,18,10,11,21,2,3,4,25,6,7,8,36,10,11,39,13,25,2,3,4,18,6,7,8,22,10,
%U 11
%N Least positive integer k <= n such that 2*k^2-1 is a prime and n - k is a square, or 0 if such an integer k does not exist.
%C By the conjecture in A230494, we should have a(n) > 0 for all n > 1.
%H Zhi-Wei Sun, <a href="/A230546/b230546.txt">Table of n, a(n) for n = 1..10000</a>
%e a(4) = 3 since neither 4 - 1 = 3 nor 4 - 2 = 2 is a square, but 4 - 3 = 1 is a square and 2*3^2 - 1 = 17 is a prime.
%t SQ[n_]:=IntegerQ[Sqrt[n]]
%t Do[Do[If[PrimeQ[2k^2-1]&&SQ[n-k],Print[n," ",k];Goto[aa]],{k,1,n}];
%t Print[n," ",0];Label[aa];Continue,{n,1,60}]
%t lpik[n_]:=Module[{k=1},While[!PrimeQ[2k^2-1]||!IntegerQ[Sqrt[n-k]],k++];k]; Join[{0},Array[lpik,60,2]] (* _Harvey P. Dale_, Aug 04 2021 *)
%Y Cf. A000040, A000290, A066049, A230351, A230362, A230493, A230494.
%K nonn
%O 1,2
%A _Zhi-Wei Sun_, Oct 23 2013
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