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

1,2

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.

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}]

Crossrefs

Cf. A090872, A235390.

Sequence in context: A058435 A151606 A176939 * A322095 A158346 A018854

Adjacent sequences: A070691 A070692 A070693 * A070695 A070696 A070697

Keyword

nonn

Author

Robert G. Wilson v, May 13 2002

Extensions

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

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

Status

approved