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%I #18 Aug 03 2014 14:01:39
%S 17,37,457,601,701,877,997,2017,3037,3257,4957,5237,5701,10601,11257,
%T 11677,14737,15217,16001,17317,17837,21577,22157,24677,29717,34057,
%U 39157,39937,41201,50777,52201,53101,75277,78101,79201,89917,91097,93001,94201,96137
%N Primes of the form (n^2+1)/26.
%C Equivalently, primes of the form (K^2 + (K+1)^2)/13. The
%C connection to the primes of the form (m^2+1)/26 is given by m=2*K+1 (m is necessarily odd).
%C The corresponding m=m(n) values are given in A208293(n).
%C Equivalently, primes of the form (4*T(K)+1)/13, with the
%C corresponding triangular numbers T(K):=A000217(K), for
%C K=K(n)=(m(n)-1)/2, given in A208294(n).
%C For n>=2 the smallest positive representative of the class of
%C nontrivial solutions of the congruence x^2==1 (Modd a(n)) is
%C x=m(n). The trivial solution is the class with representative x=1, which also includes -1. For the prime
%C 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.
%C These primes with corresponding m values are such that floor(m(n)^2/p(n)) = 5^2, n>=1.
%H Vincenzo Librandi, <a href="/A208292/b208292.txt">Table of n, a(n) for n = 1..2000</a>
%F 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).
%e a(3)=457, m(3)=A208293(3)=109. T(K(3))=A000217((109-1)/2)=
%e A000217(54)=A208294(3)=1485.
%t Select[(Range[2000]^2 + 1)/26, PrimeQ] (* _T. D. Noe_, Feb 28 2012 *)
%Y Cf. A207337, A207339 (case floor(m^2/p)=3^2); A129307, A027862, A002731 (case floor(m^2/p)=1^2).
%K nonn
%O 1,1
%A _Wolfdieter Lang_, Feb 27 2012
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