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%I #21 Aug 26 2023 23:26:31
%S 0,0,0,0,3,0,5,2,3,2,7,3,7,2,3,2,7,3,13,2,3,5,7,3,7,2,5,5,13,7,13,5,5,
%T 2,7,3,7,5,3,2,13,3,31,2,3,17,7,3,13,2,11,5,7,7,13,2,5,11,13,7,19,5,5,
%U 2,7,3,7,11,3,2,13,13,7,17,5,2,7,3,19,5
%N Least prime p such that n-(p*n'-1) and n+(p*n'-1) are both prime where n' = (3+(-1)^n)/2, or 0 if no such prime p exists.
%C Conjecture: 0 < a(n) < sqrt(2*n)*log(5*n) for all n > 6.
%C See also A261627.
%C Verified up to 10^9. - _Mauro Fiorentini_, Jul 05 2023
%C Conjecture verified for n < 1.2 * 10^12. Also, the 5 inside the log function can probably be replaced by 4.26. - _Jud McCranie_, Aug 26 2026
%H Zhi-Wei Sun, <a href="/A261628/b261628.txt">Table of n, a(n) for n = 1..10000</a>
%H Zhi-Wei Sun, <a href="http://arxiv.org/abs/1211.1588">Conjectures involving primes and quadratic forms</a>, arXiv:1211.1588 [math.NT], 2012-2015.
%e a(43) = 31 since 31, 43-(31-1) = 13 and 43+(31-1) = 73 are all prime.
%e a(72) = 13 since 13, 72-(2*13-1) = 47 and 72+(2*13-1) = 97 are all prime.
%t Do[Do[If[PrimeQ[n-(3+(-1)^n)/2*Prime[k]+1]&&PrimeQ[n+(3+(-1)^n)/2*Prime[k]-1],Print[n," ",Prime[k]];Goto[aa]],{k,1,PrimePi[2n/(3+(-1)^n)]}];Print[n," ",0];Label[aa];Continue,{n,1,80}]
%Y Cf. A000040, A002372, A002375, A046927, A261627.
%K nonn
%O 1,5
%A _Zhi-Wei Sun_, Aug 27 2015
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