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 (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, ...