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
Keywords
Examples
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.
Links
- K. D. Bajpai, Table of n, a(n) for n = 1..10000
Programs
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Magma
[k : p in PrimesUpTo (10000) | IsPrime(p+2) and IsPrime(k) where k is ((p + p + 2)^2 + 1)];
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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);
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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
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PARI
forprime(p = 1,10000, if(isprime(p+2) && isprime((p + p + 2)^2 + 1), print1(( (p + p + 2)^2 + 1), ", ")));
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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
Comments