A253178 - OEIS

%I #58 Apr 13 2015 05:10:50

%S 1,1,1,1,1,1,1,3,1,1,47,1,1,1,1,2,1,2,1,1,3,1,1,1,2729,1,1,2,1,2,175,

%T 1,1,1,1,1,1,3,3,3,43,1,1,2,1,1,3,2,1,1,3,1,11,1,1,4,1,2,1,1,3,2,1,1,

%U 1,1,192275,2,1233,1,3,5,51,1,1,1,1,286,1,1,755,2,1,4,1,6,1,2

%N Least k>=1 such that 2*A007494(n)^k+1 is prime.

%C If n == 1 (mod 3), then for every positive integer k, 2*n^k+1 is divisible by 3 and cannot be prime (unless n=1). Thus we restrict the domain of this sequence to A007494 (n which is not in the form 3j+1).

%C Conjecture: a(n) is defined for all n.

%C a(145) > 200000, a(146) .. a(156) = {1, 1, 66, 1, 4, 3, 1, 1, 1, 1, 6}, a(157) > 100000, a(158) .. a(180) = {2, 1, 2, 11, 1, 1, 3, 321, 1, 1, 3, 1, 2, 12183, 5, 1, 1, 957, 2, 3, 16, 3, 1}.

%C a(n) = 1 if and only if n is in A144769.

%H Eric Chen, <a href="/A253178/b253178.txt">Table of n, a(n) for n = 1..144</a>

%F a(n) = A119624(A007494(n)).

%t A007494[n_] := 2n - Floor[n/2];

%t Table[k=1; While[!PrimeQ[2*A007494[n]^k+1], k++]; k, {n, 1, 144}]

%o (PARI) a007494(n) = n+(n+1)>>1;

%o a(n) = for(k=1, 2^24, if(ispseudoprime(2*a007494(n)^k+1),return(k)));

%Y Cf. A138066, A138067, A255707, A250200, A119624, A119591, A040076, A046067.

%K nonn,hard

%O 1,8

%A _Eric Chen_, Mar 20 2015