cp's OEIS Frontend

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.

The corresponding primes are gven in A208292, where equivalent formulations are found.

The indices of these triangular numbers are given by (A208293(n)-1)/2.