A143012 Numbers of the form (4^p + 2^p + 1)/7, where p > 3 is prime.

151, 2359, 599479, 9588151, 2454285751, 39268347319, 10052678938039, 41175768098368951, 658812288653553079, 2698495133088002829751, 690814754065816531725751, 11053036065049294753459639, 2829577232652317876553477559, 11589948344943812957569751412151

Offset: 1

Author

Vladimir Shevelev, Jul 15 2008, Jul 21 2008

Keywords

• nonn

Comments

If 8^p-1 is squarefree then the terms of the sequence are either primes (A000040) or overpseudoprimes to base 2 (A141232). In particular, composite numbers of the sequence are strong pseudoprimes to base 2 (A001262). E.g., a(5)=2454285751 is A001262(1828).

Links

• V. Shevelev, Process of "primoverization" of numbers of the form a^n-1, arXiv:0807.2332 [math.NT], 2008.

Crossrefs

Cf. A001262, A141232, A000040, A126614.

Programs

Maple

p:=ithprime: seq((4^p(n)+2^p(n)+1)*1/7, n=3..14); # Emeric Deutsch, Aug 16 2008

Mathematica

(4^#+2^#+1)/7&/@Prime[Range[3,30]] (* Harvey P. Dale, Feb 19 2013 *)

Extensions

Extended by Emeric Deutsch, Aug 16 2008

More terms from Harvey P. Dale, Feb 19 2013