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A070694 Numbers b such that b+1, b^2+1, b^4+1, b^8+1 and b^16+1 are primes. 8
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 (list; graph; refs; listen; history; text; internal format)
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}]
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 *)
CROSSREFS
Sequence in context: A058435 A151606 A176939 * A322095 A158346 A018854
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

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Last modified July 24 22:37 EDT 2024. Contains 374585 sequences. (Running on oeis4.)