A139780 Average of twin primes of the form p1^3 + p2^2, where p1 < p2 are twin primes.

38318210940, 68484878220, 143165125680, 6353554336290, 75041090138100, 91851874324800, 116366750976990, 118525130067690, 368776631152800, 374826155288910, 431041855258500, 585102141663000, 767853933976740, 834602006112360, 845499208101600, 1560061877051100

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, May 16 2008

Keywords

• nonn

Examples

			38318210940 = 3371^3 + 3373^2 is a term since both (3371, 3373) and (38318210939, 38318210941) are twin primes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001097, A001359, A006512, A014574.

Cf. A138716, A138755, A139777.

Programs

Magma

[q:k in [1..10000]|IsPrime((NthPrime(k)+2)) and IsPrime(q-1)and IsPrime(q+1) where q is NthPrime(k)^3+ (NthPrime(k)+2)^2]; // Marius A. Burtea, Dec 22 2019

Mathematica

a={};Do[p1=Prime[n];p2=Prime[n+1];pp=p1^3+p2^2;If[(p2-p1)==2&&PrimeQ[pp-1]&&PrimeQ[pp+1],AppendTo[a,pp]],{n,10^4}];Print[a];
Select[#[[1]]^3+#[[2]]^2&/@Select[Partition[Prime[Range[15000]],2,1],#[[2]] - #[[1]]==2&],AllTrue[#+{1,-1},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 01 2021 *)

Extensions

More terms from Amiram Eldar, Dec 22 2019