A138716 Primes p2 such that p1^2 + p2^3 is an average of twin primes and p1 < p2 are consecutive primes.

29, 107, 1481, 1613, 2393, 2879, 4421, 5021, 5519, 5573, 6269, 7817, 8447, 9629, 11489, 11981, 12011, 17159, 17573, 18461, 19961, 21713, 23021, 23291, 23747, 24917, 26339, 27947, 29021, 29201, 29663, 30893, 32063, 32717, 34217, 34589, 35159, 36527, 36899, 44753

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, 23^2 + 29^3 = 24918, and (24917, 24919) are twin primes.

Mathematica

a={}; Do[p1=Prime[n]; p2=Prime[n+1]; pp=p1^2+p2^3; If[PrimeQ[pp-1]&&PrimeQ[pp+1], AppendTo[a, p2]], {n, 16^3}]; Print[a];
Select[Partition[Prime[Range[5000]], 2, 1], AllTrue[#[[1]]^2+#[[2]]^3+{1, -1}, PrimeQ]&] [[All, 2]] (* Harvey P. Dale, Oct 29 2022 *)

Prog

(Magma) [NthPrime(k+1):k in [1..5000]| IsPrime(q-1) and IsPrime(q+1) where q is NthPrime(k)^2+ NthPrime(k+1)^3]; // Marius A. Burtea, Dec 22 2019

Crossrefs

Cf. A001097, A001359, A006512, A014574.

Cf. A138755, A139777, A139780.

Sequence in context: A233050 A142176 A115272 * A276776 A142194 A139495

Adjacent sequences: A138713 A138714 A138715 * A138717 A138718 A138719

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 15 2008

Extensions

More terms from Amiram Eldar, Dec 22 2019

Status

approved