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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A343454 Numbers k such that k^2+2*A001414(k) and k^2-2*A001414(k) are primes.

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%I A343454 #8 Apr 15 2021 23:42:06
%S A343454 21,33,35,39,111,339,473,629,735,779,795,801,959,1025,1119,1149,1245,
%T A343454 1253,1281,1575,1589,1695,1851,1919,1961,1985,2199,2315,2523,2561,
%U A343454 2681,2759,3003,3065,3189,3233,3315,3443,3893,3983,4175,4299,4359,4375,4455,4503,4693,4925,5247,5585,5609,5703
%N A343454 Numbers k such that k^2+2*A001414(k) and k^2-2*A001414(k) are primes.
%C A343454 Square roots of squares in A050705.
%C A343454 All terms are odd.
%C A343454 Includes 3*p if p, 9*p^2+2*p+6 and 9*p^2-2*p-6 are all primes; the generalized Bunyakovsky conjecture implies there are infinitely many of these.
%H A343454 Robert Israel, <a href="/A343454/b343454.txt">Table of n, a(n) for n = 1..10000</a>
%e A343454 a(3) = 35 is a term because A001414(35) = 12 and 35^2-2*12 = 1201 and 35^2+2*12 = 1249 are primes.
%p A343454 spf:= n -> add(t[1]*t[2],t=ifactors(n)[2]):
%p A343454 filter:= proc(n) local s; s:= spf(n); isprime(n^2-2*s) and isprime(n^2+2*s) end proc:
%p A343454 select(filter, [seq(i,i=1..10000,2)]);
%Y A343454 Cf. A001414, A050705.
%K A343454 nonn
%O A343454 1,1
%A A343454 _J. M. Bergot_ and _Robert Israel_, Apr 15 2021