A139776 Average of twin primes p3 such that p1^2 + p2^3=p3 and p1^3 + p2^2 = p4, p3 and p4 are average of twin primes. p1 and p2 consecutive primes, p1 < p2.

24918, 9270440598450720, 1151315644373474442978, 1166412457712602408182, 1408820228836430919078, 1611036311504881881342, 1839287439769397002278, 1876396650678820877442, 2541675503832771774858, 3760334521638661478022, 13232238501319295512260, 19086564229432581494760, 30269637404459759488308

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..120

Example

24918 is a term since p1 = 23 and p2 = 29 are consecutive primes such that p1^2 + p2^3 = 24918 and p1^3 + p2^2 = 13008 are averages of 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, p3]], {n, 13^5}]; Print[a];

Prog

(PARI) testA139776(p, q)={my(p3=p^2+q^3, p4=p^3+q^2); ispseudoprime(p3-1)&&ispseudoprime(p3+1)&&ispseudoprime(p4-1)&&ispseudoprime(p4+1)} p=3; forprime(q=5, 1e7, if(testA139776(p, q), print1(p^2+q^3", ")); p=q)

Crossrefs

Cf. A001097, A001359, A006512, A014574, A138763.

Sequence in context: A110599 A199857 A138717 * A214013 A252846 A031651

Adjacent sequences: A139773 A139774 A139775 * A139777 A139778 A139779

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 16 2008

Extensions

Program and more terms from Charles R Greathouse IV Jul 27 2009

Status

approved