OFFSET
1,1
COMMENTS
Equivalently, primes of the form (K^2 + (K+1)^2)/5. The connection to the primes of the form (m^2+1)/10 is given by m=2*K+1 (m is necessarily odd). The corresponsding m=m(n) values are given in A002733(n).
Equivalently, primes of the form (4*T(K)+1)/5, with the corresponding triangular numbers T(K):=A000217(K), for K(n)=(m(n)-1)/2, given in A207339(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)=5 the smallest positive nontrivial solution is 3 (see A027862(1) with A002731(1)). Such a nontrivial smallest positive representative exists for each unique class of solutions of this congruence Modd p for any prime p of the form 4*k+1, given in A002144. Here the subset with k=k(n)=(a(n)-1)/4 appears, namely 1, 4, 7, 13, 18, 27, 34, 70,... For Modd n see a comment on A203571.
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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, namely A002733(n).
EXAMPLE
PROG
(Haskell)
a207337 n = a207337_list !! (n-1)
a207337_list = f a002522_list where
f (x:xs) | m == 0 && a010051 y == 1 = y : f xs
| otherwise = f xs
where (y, m) = divMod x 10
-- Reinhard Zumkeller, Apr 06 2012
CROSSREFS
KEYWORD
nonn
AUTHOR
Wolfdieter Lang, Feb 27 2012
STATUS
approved