# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a253178
Showing 1-1 of 1

%I A253178 #58 Apr 13 2015 05:10:50
%S A253178 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 A253178 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 A253178 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 A253178 Least k>=1 such that 2*A007494(n)^k+1 is prime.
%C A253178 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 A253178 Conjecture: a(n) is defined for all n.
%C A253178 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 A253178 a(n) = 1 if and only if n is in A144769.
%H A253178 Eric Chen, <a href="/A253178/b253178.txt">Table of n, a(n) for n = 1..144</a>
%F A253178 a(n) = A119624(A007494(n)).
%t A253178 A007494[n_] := 2n - Floor[n/2];
%t A253178 Table[k=1; While[!PrimeQ[2*A007494[n]^k+1], k++]; k, {n, 1, 144}]
%o A253178 (PARI) a007494(n) = n+(n+1)>>1;
%o A253178 a(n) = for(k=1, 2^24, if(ispseudoprime(2*a007494(n)^k+1),return(k)));
%Y A253178 Cf. A138066, A138067, A255707, A250200, A119624, A119591, A040076, A046067.
%K A253178 nonn,hard
%O A253178 1,8
%A A253178 _Eric Chen_, Mar 20 2015

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE