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A261889 Primes that are the square of the sum of a twin prime pair plus 1. 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 22 12:52 EDT 2019. Contains 327307 sequences. (Running on oeis4.)