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%I #12 Oct 28 2024 09:34:42
%S 3,13,3,3,5,3,17,3,163,3,3,109,3,13,19,5,3,3,1879,3,13,379,7,1531,7,5,
%T 337,5,3,61,19,3,23,3,11,16417,163,23,3,5,3,3,3,5
%N Minimum number k>0 such that ((2n+1)^k - (2n-1)^k)/2 is prime.
%C All a(n) are primes. Corresponding minimal primes of the form ((2n+1)^k - (2n-1)^k)/2 are {13, 609554401, 109, 193, 51001, 433, 44937854708156010721, 769, ...}.
%C a(46)-a(49) are 17, 5, 31, 3. a(51)-a(61) are 109, 5, 7, 89, 13, 3, 31, 53, 5, 3, 5. a(63)-a(69) are 3, 7, 19, 5, 167, 163, 293. a(71)-a(74) are 3, 3407, 3, 3. a(76)-a(77) are 3, 19.
%C a(45), a(50), a(62), a(70), a(75) are currently unknown.
%C a(45) > 30000. - _Max Alekseyev_, May 18 2010
%t s={};Do[k=1;Until[PrimeQ[((2n+1)^k-(2n-1)^k)/2],k++];AppendTo[s,k] ,{n,35}];s (* _James C. McMahon_, Oct 27 2024 *)
%Y Cf. A028491, A121877.
%K hard,more,nonn
%O 1,1
%A _Alexander Adamchuk_, Sep 14 2006, Sep 17 2006, Oct 07 2006
%E a(36)=16417 from _Max Alekseyev_, May 11 2010