cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A090872 a(n) is the smallest number m greater than 1 such that m^(2^k)+1 for k=0,1,...,n are primes.

Original entry on oeis.org

2, 2, 2, 2, 2, 7072833120, 2072005925466, 240164550712338756
Offset: 0

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Author

Farideh Firoozbakht, Jan 31 2004

Keywords

Comments

The first five terms of this sequence correspond to Fermat primes.
Note that 7072833120 is not the smallest base to give at least six possibly nonconsecutive k values. For example, 292582836^(2^k) + 1 is prime for k = 0,1,2,3,4,7. - Jeppe Stig Nielsen, Sep 18 2022

Examples

			a(5)=7072833120 because 7072833120^2^k+1 for k=0,1,2,3,4,5 are primes.
		

Crossrefs

All solutions for fixed n: A006093 (n=0), A070689 (n=1), A070325 (n=2), A070655 (n=3), A070694 (n=4), A235390 (n=5), A335805 (n=6), A337364 (n=7).

Extensions

a(6) from Jens Kruse Andersen, May 06 2007
a(7) from Kellen Shenton, Aug 13 2020

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

Original entry on oeis.org

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

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Author

Robert G. Wilson v, May 13 2002

Keywords

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

Crossrefs

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

A335805 Numbers b such that b^(2^i) + 1 is prime for i = 0...6.

Original entry on oeis.org

1, 2072005925466, 5082584069416, 12698082064890, 29990491969260, 46636691707050, 65081025897426, 83689703895606, 83953213480290, 105003537341346, 105699143244090, 107581715369910, 111370557491826, 111587899569066, 128282713771996, 133103004825210
Offset: 1

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Author

Jeppe Stig Nielsen, Aug 14 2020

Keywords

Comments

Explicitly, for each b, the seven numbers b+1, b^2+1, b^4+1, b^8+1, b^16+1, b^32+1, and b^64+1 must be primes (generalized Fermat primes).
The first term greater than 1 such that b^(2^7) + 1 is also prime, is 240164550712338756, see A337364. - Jeppe Stig Nielsen, Aug 25 2020

Crossrefs

A337364 Numbers b such that b^(2^i) + 1 is prime for i = 0...7.

Original entry on oeis.org

1, 240164550712338756, 3686834112771042790, 6470860179642426900, 7529068955648085700, 10300630358100537120, 16776829808789151280, 17622040391833711780, 19344979062504927000, 23949099004395080026, 25348938242408650240, 30262840543567048476, 35628481193915651646
Offset: 1

Views

Author

Jeppe Stig Nielsen, Aug 25 2020

Keywords

Comments

Explicitly, for each b, the eight numbers b+1, b^2+1, b^4+1, b^8+1, b^16+1, b^32+1, b^64+1, and b^128+1 must be primes (generalized Fermat primes).

Crossrefs

Extensions

a(10)-a(12) from Jeppe Stig Nielsen, Sep 04 2020
a(13) found by Rob Gahan added by Jeppe Stig Nielsen, Feb 15 2021
Showing 1-4 of 4 results.