cp's OEIS Frontend

A261889 Primes that are the square of the sum of a twin prime pair plus 1.

%I A261889 #23 Sep 08 2022 08:46:13
%S A261889 577,1297,7057,14401,41617,90001,147457,156817,484417,746497,1299601,
%T A261889 1742401,2702737,2944657,4260097,5308417,6051601,6780817,8785297,
%U A261889 10497601,14107537,15210001,16451137,17438977,18147601,29419777,38937601,45968401,51322897,56791297
%N A261889 Primes that are the square of the sum of a twin prime pair plus 1.
%C A261889 Alternatively: Primes of the form (p + q)^2 + 1 where p and q are twin primes.
%C A261889 All the terms are congruent to 1 (mod 3).
%H A261889 K. D. Bajpai, <a href="/A261889/b261889.txt">Table of n, a(n) for n = 1..10000</a>
%e A261889 577 appears in the sequence because it is a prime resulting from twin prime pair (11,13): (11 + 13)^2 + 1 = 577.
%e A261889 7057 appears in the sequence because it is a prime resulting from twin prime pair (41,43): (41 + 43)^2 + 1 = 7057.
%p A261889 A261889:= proc() local a, b, d; a:= ithprime(n); b:=a+2; d:=(a+b)^2+1; if isprime(b)and isprime(d) then return (d): fi; end: seq(A261889 (), n=1..10000);
%t A261889 A261889 = {}; Do[p1 = Prime[n]; p2 = p1 + 2; p = (p1 + p2)^2 + 1; If[PrimeQ[p2] &&  PrimeQ[p], AppendTo[A261889, p]], {n, 1, 10000}]; A261889
%o A261889 (PARI) forprime(p = 1,10000, if(isprime(p+2) && isprime((p + p + 2)^2 + 1), print1(( (p + p + 2)^2 + 1), ", ")));
%o A261889 (PARI) list(lim)=my(v=List(),t,p=2); forprime(q=3,sqrtint(lim\1-1)\2+1, if(q-p==2 && isprime(t=(p+q)^2+1), listput(v,t)); p=q); Vec(v) \\ _Charles R Greathouse IV_, Sep 06 2015
%o A261889 (Magma) [k : p in PrimesUpTo (10000) | IsPrime(p+2) and IsPrime(k) where k is ((p + p + 2)^2 + 1)];
%Y A261889 Cf. A000040, A051779, A054735.
%K A261889 nonn
%O A261889 1,1
%A A261889 _K. D. Bajpai_, Sep 05 2015