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

1,1

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A001097, A001359, A006512, A014574.

Cf. A138716, A139777, A139780.

Sequence in context: A190826 A045688 A084223 * A265445 A370339 A316333

Adjacent sequences: A138752 A138753 A138754 * A138756 A138757 A138758

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 15 2008

Extensions

More terms from Amiram Eldar, Dec 22 2019

Status

approved