OFFSET
1,1
COMMENTS
Equivalently, primes of the form (K^2 + (K+1)^2)/13. The
connection to the primes of the form (m^2+1)/26 is given by m=2*K+1 (m is necessarily odd).
The corresponding m=m(n) values are given in A208293(n).
Equivalently, primes of the form (4*T(K)+1)/13, with the
corresponding triangular numbers T(K):=A000217(K), for
K=K(n)=(m(n)-1)/2, given in A208294(n).
For n>=2 the smallest positive representative of the class of
nontrivial solutions of the congruence x^2==1 (Modd a(n)) is
x=m(n). The trivial solution is the class with representative x=1, which also includes -1. For the prime
a(1)=17 the nontrivial solution is 13 (see A002733(2)). Unique nontrivial smallest positive representatives exist for the solutions for any prime of the form 4*k+1, given in A002144. Here the subset with k=k(n)=(a(n)-1)/4 appears, namely 4,9,114,150,175,219,.... For Modd n see a comment on A203571.
These primes with corresponding m values are such that floor(m(n)^2/p(n)) = 5^2, n>=1.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..2000
FORMULA
a(n) is the n-th member of the increasingly ordered list of primes of the form (m^2+1)/10, where m=m(n) is necessarily an odd integer, the positive one is A208293(n).
MATHEMATICA
Select[(Range[2000]^2 + 1)/26, PrimeQ] (* T. D. Noe, Feb 28 2012 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Wolfdieter Lang, Feb 27 2012
STATUS
approved