A138755 Primes p2 such that p1^3 + p2^2 is an average of twin primes and p1 < p2 are consecutive primes.

29, 2081, 2357, 3373, 3727, 4013, 4093, 5233, 6007, 7829, 15559, 15797, 16319, 17123, 18523, 20143, 22037, 23071, 25261, 26293, 28019, 28289, 33797, 39499, 41627, 42181, 42929, 45121, 48533, 48823, 49123, 50417, 52697, 54629, 57973, 58897, 60887, 62761, 64381

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, May 15 2008

Keywords

• nonn

Examples

			29 is a term since 23 and 29 are consecutive primes, 23^3 + 29^2 = 13008, and (13007, 13009) are twin primes.
		

Links

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

Crossrefs

Cf. A001097, A001359, A006512, A014574.

Cf. A138716, A139777, A139780.

Programs

Magma

[NthPrime(k+1):k in [1..7000]| IsPrime(q-1) and IsPrime(q+1) where q is NthPrime(k)^3+ NthPrime(k+1)^2]; // Marius A. Burtea, Dec 22 2019

Mathematica

a={};Do[p1=Prime[n];p2=Prime[n+1];pp=p1^3+p2^2;If[PrimeQ[pp-1]&&PrimeQ[pp+1],AppendTo[a,p2]],{n,16^3}];Print[a];
Select[Partition[Prime[Range[6500]],2,1],AllTrue[#[[1]]^3+#[[2]]^2+{1,-1},PrimeQ]&][[All,2]] (* Harvey P. Dale, Aug 29 2021 *)

Extensions

More terms from Amiram Eldar, Dec 22 2019