A070694 Numbers b such that b+1, b^2+1, b^4+1, b^8+1 and b^16+1 are primes.

1, 2, 337536, 585106, 602056, 2071960, 11861410, 20706120, 54020170, 72696726, 87584646, 89445636, 95895930, 98583340, 98595070, 112204200, 205739220, 279448296, 292582836, 337969690, 349672456, 432972780, 437874186, 474186576, 479631880, 483333426, 621777466, 643697776

Offset: 1

Author

Robert G. Wilson v, May 13 2002

Keywords

• nonn

Comments

The first term greater than 1 such that b^32+1 is also a prime is a(173) = 7072833120, see A235390. - Alex Ratushnyak, Jan 02 2014, comment extended by Jeppe Stig Nielsen, Aug 18 2020

The term a(2)=2 corresponds to the five classical Fermat primes. - Jeppe Stig Nielsen, Aug 18 2020

Links

• Jeppe Stig Nielsen, Table of n, a(n) for n = 1..1000 (calculated by Yves Gallot).
• Yves Gallot, GFP (Generalized Fermat Progressions) / gfp5, software for calculating this sequence.

Crossrefs

Cf. A090872, A235390.

Programs

Mathematica

Do[ If[ PrimeQ[n + 1] && PrimeQ[n^2 + 1] && PrimeQ[n^4 + 1] && PrimeQ[n^8 + 1] && PrimeQ[n^16 + 1], Print[n]], {n, 1, 10^7}]
Select[Range[21*10^5],AllTrue[#^2^Range[0,4]+1,PrimeQ]&] (* The program generates the first six terms of the sequence. *) (* Harvey P. Dale, Jun 02 2024 *)

Extensions

a(7)-a(24) from Donovan Johnson, Dec 02 2009

a(25)-a(28) from Alex Ratushnyak, Jan 02 2014