A090873 -id:A090873 - cp's OEIS frontend

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

2, 2, 2, 2, 2, 7072833120, 2072005925466, 240164550712338756

Offset: 0

Farideh Firoozbakht, Jan 31 2004

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

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

PrimeGrid, Generalized Fermat Progression Search
Carlos Rivera, Puzzle 137. Product of primes + 1, a square, The Prime Puzzles and Problems Connection.
Carlos Rivera, Prime Puzzle 399. Some more terms, The Prime Puzzles and Problems Connection.

Cf. A019434, A000215.
Cf. A090873, A090874, A090875.
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).

a(6) from Jens Kruse Andersen, May 06 2007

a(7) from Kellen Shenton, Aug 13 2020

A090874 a(n) is the smallest number m such that m^2^k + (m+1)^2^k is prime for k=0..n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1806390369, 218327374070, 3697211121741701604

Offset: 0

Farideh Firoozbakht, Feb 06 2004

The first five terms of this sequence correspond to Fermat primes.

			a(5)=1806390369 because this is the smallest number m such that m^2^k + (m+1)^2^k is prime for k=0,1,2,3,4 and 5.

Cf. A090872, A090873, A019434, A000215.

a(6) found by Kellen Shenton added by Jeppe Stig Nielsen, Mar 28 2022

a(7) from Kellen Shenton, Aug 27 2022

A090875 a(n) is the smallest number m such that m^(2^k) + 2^(2^k) is prime for k=0,1,...,n.

Original entry on oeis.org

1, 1, 1, 1, 1, 2321204055, 37185086099807

Offset: 0

Farideh Firoozbakht, Feb 06 2004

nonn

The first five terms of this sequence correspond to Fermat primes.

According to the answers to Prime Puzzle 399 (see link), a(6) is larger than 2.3*10^12. - M. F. Hasler, Aug 02 2007

			a(5)=2321204055 because 2321204055 is the smallest number m such that m^(2^k) + 2^(2^k) is prime for k=0,1,2,3,4 and 5.

Carlos Rivera (ed.), Puzzle 399. Some more terms, The Prime Puzzles and Problems Connection.

Cf. A090872, A090873, A090874.

a(6) found by Kellen Shenton sent in by Jeppe Stig Nielsen, Apr 06 2022

cp's OEIS Frontend

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

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A090874 a(n) is the smallest number m such that m^2^k + (m+1)^2^k is prime for k=0..n.

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Extensions

A090875 a(n) is the smallest number m such that m^(2^k) + 2^(2^k) is prime for k=0,1,...,n.

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Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions