OFFSET
1,1
COMMENTS
The corresponding primes (n^2+1)/26 are given in A208292(n).
a(n) is the smallest positive representative of the class of
nontrivial solutions of the congruence x^2==1 (Modd A208292(n)), if n>=2. The trivial solution is the class with representative x=1, which also includes -1. For Modd n see a comment on A203571. For n=1: a(1) = 21 == 13 (Modd 17), and 13 is the smallest positive solution >1.
The unique class of nontrivial solutions of the congruence x^2==1 (Modd p), with p an odd prime, exists for any p of the form 4*k+1, given in A002144. Here a subset of these primes is covered, the ones for k=k(n)=(a(n)^2-25)/(4*26). These values are 4, 9, 114, 150, 175, 219, ...
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
EXAMPLE
a(3)=109 because (109^2+1)/26 = 457 is prime.
109 = sqrt(26*457-1) = sqrt(8*1485+1).
MATHEMATICA
Select[Range[10000], PrimeQ[(#^2 + 1)/26] &] (* T. D. Noe, Feb 28 2012 *)
PROG
(PARI) is(n)=isprime((n^2+1)/26) \\ Charles R Greathouse IV, May 22 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Wolfdieter Lang, Feb 27 2012
STATUS
approved