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a(n) = A244915(n)^2 + A244915(n+1)^2.
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%I #9 Dec 01 2021 11:37:57

%S 2,5,13,73,89,29,53,113,233,173,229,241,17,37,61,41,97,181,101,197,

%T 277,337,257,401,409,109,149,193,313,269,389,293,733,829,461,397,157,

%U 137,457,541,941,857,641,661,877,1097,281,349,373,449,521,317,421,709,509

%N a(n) = A244915(n)^2 + A244915(n+1)^2.

%C All terms are prime and distinct.

%H Rémy Sigrist, <a href="/A349735/b349735.txt">Table of n, a(n) for n = 0..10000</a>

%e a(4) = A244915(4)^2 + A244915(5)^2 = 8^2 + 5^2 = 89.

%o (PARI) s=0; v=1; for (n=0, 54, for (w=1, oo, p=v^2+w^2; if (!bittest(s, p) && isprime(p), print1(p ", "); s+=2^p; v=w; break)))

%Y Cf. A244915.

%K nonn,look

%O 0,1

%A _Rémy Sigrist_, Nov 28 2021