A138715 Primes p1 such that p1^2+p2^3=pp are average of twin primes. p1 and p2 consecutive primes, p1 < p2.

23, 103, 1471, 1609, 2389, 2861, 4409, 5011, 5507, 5569, 6263, 7793, 8443, 9623, 11483, 11971, 12007, 17137, 17569, 18457, 19949, 21701, 23017, 23279, 23743, 24907, 26321, 27943, 29017, 29191, 29641, 30881, 32059, 32713, 34213, 34583, 35153, 36523, 36887

Offset

1,1

Links

Table of n, a(n) for n=1..39.

Mathematica

a={}; Do[p1=Prime[n]; p2=Prime[n+1]; pp=p1^2+p2^3; If[PrimeQ[pp-1]&&PrimeQ[pp+1], AppendTo[a, p1]], {n, 16^3}]; Print[a];
atpQ[n_]:=Module[{c=First[n]^2+Last[n]^3}, And@@PrimeQ[{c-1, c+1}]]; Transpose[Select[Partition[Prime[Range[5000]], 2, 1], atpQ]][[1]] (* Harvey P. Dale, Sep 11 2011 *)

Crossrefs

Sequence in context: A142192 A129918 A240839 * A096324 A044274 A044655

Adjacent sequences: A138712 A138713 A138714 * A138716 A138717 A138718

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 15 2008

Extensions

More terms from Harvey P. Dale, Sep 11 2011

Typo in a(39) corrected by Seth A. Troisi, May 13 2022

Status

approved