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A268108
Even indices of Pell numbers of the form x^2 + y^2 where x, y > 0.
0
2, 10, 50, 58, 106, 226, 250, 290, 346, 514, 562, 842, 866, 914
OFFSET
1,1
COMMENTS
Sequence focuses on the even Pell numbers.
Corresponding Pell numbers are 2, 2378, 4866752642924153522, 5616228332641321147898, 13264095873479197467931567359068050319018, ...
First differences are 8, 40, 8, 48, 120, 24, 40, ...
EXAMPLE
2 is a term since A000129(2) = 2 = 1^2 + 1^2.
10 is a term since A000129(10) = 2378 = 13^2 + 47^2.
50 is a term since A000129(50) = 4866752642924153522 = 101254909^2 + 2203746829^2.
PROG
(PARI) a000129(n) = sum(k=0, n, binomial(n, 2*k+1) * 2^k);
isA000404(n) = {for(i=1, #n=factor(n)~%4, n[1, i]==3 && n[2, i]%2 && return); n && ( vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2))}
for(n=1, 1e3, if(isA000404(a000129(2*n)), print1(2*n, ", ")));
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Altug Alkan, Jan 26 2016
EXTENSIONS
a(9)-a(14) from Jinyuan Wang, Aug 14 2022
STATUS
approved