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

577, 1297, 7057, 14401, 41617, 90001, 147457, 156817, 484417, 746497, 1299601, 1742401, 2702737, 2944657, 4260097, 5308417, 6051601, 6780817, 8785297, 10497601, 14107537, 15210001, 16451137, 17438977, 18147601, 29419777, 38937601, 45968401, 51322897, 56791297

Offset

1,1

Comments

Alternatively: Primes of the form (p + q)^2 + 1 where p and q are twin primes.

All the terms are congruent to 1 (mod 3).

Links

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Example

577 appears in the sequence because it is a prime resulting from twin prime pair (11,13): (11 + 13)^2 + 1 = 577.
7057 appears in the sequence because it is a prime resulting from twin prime pair (41,43): (41 + 43)^2 + 1 = 7057.

Maple

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);

Mathematica

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

Prog

(PARI) forprime(p = 1, 10000, if(isprime(p+2) && isprime((p + p + 2)^2 + 1), print1(( (p + p + 2)^2 + 1), ", ")));
(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
(Magma) [k : p in PrimesUpTo (10000) | IsPrime(p+2) and IsPrime(k) where k is ((p + p + 2)^2 + 1)];

Crossrefs

Cf. A000040, A051779, A054735.

Sequence in context: A218157 A158370 A244095 * A031726 A154514 A278740

Adjacent sequences: A261886 A261887 A261888 * A261890 A261891 A261892

Keyword

nonn

Author

K. D. Bajpai, Sep 05 2015

Status

approved