A139777 Average of twin primes p4 = p1^3 + p2^2 such that p1 < p2 are consecutive primes and p3 = p1^2 + p2^3 is also an average of twin primes.

13008, 9268057799643918, 1151303780719281840798, 1166398496059056623580, 1408815704665167877050, 1611023943160530038112, 1839284737645145603808, 1876391173984974899670, 2541672151459722294708, 3760269231809150191932, 13232137801909374644760, 19086525662779517405622

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..2000

Example

13008 = 23^3 + 29^2 is a term since 23 and 29 are consecutive primes, (13007, 13009) are twin primes, 23^2 + 29^3 = 24918, and (24917, 24919) are also twin primes.

Mathematica

a={}; Do[p1=Prime[n]; p2=Prime[n+1]; p3=p1^2+p2^3; p4=p1^3+p2^2; If[PrimeQ[p3-1]&&PrimeQ[p3+1]&&PrimeQ[p4-1]&&PrimeQ[p4+1], AppendTo[a, p4]], {n, 13^5}]; Print[a];

Crossrefs

Cf. A001097, A001359, A006512, A014574.

Cf. A138716, A138755, A139780.

Sequence in context: A203910 A354510 A138762 * A031633 A015327 A210016

Adjacent sequences: A139774 A139775 A139776 * A139778 A139779 A139780

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 16 2008

Extensions

More terms from Amiram Eldar, Dec 22 2019

Status

approved