A297422 -id:A297422 - cp's OEIS frontend

A309738 Primes of the form b^210^(2k) + b*10^k + 1 for 1 <= b <= 9, k >= 0.

3, 7, 13, 31, 43, 73, 421, 2551, 6481, 8191, 250501, 4002001, 64008001, 81009001, 40000200001, 90000300001, 64000008000001, 400000000020000000001, 3600000000060000000001, 64000000000008000000000001, 90000000000000300000000000001, 250000000000000500000000000001

Offset: 1

Seiichi Manyama, Aug 15 2019

			b | Primes of the form b^2*10^(2*k) + b*10^k + 1
--+-------------------------------------------------------------
1 | 3.
2 | 7, 421, 4002001, 40000200001, 400000000020000000001, ...
3 | 13, 90000300001, 90000000000000300000000000001, ...
4 |
5 | 31, 2551, 250501, 250000000000000500000000000001, ...
6 | 43, 3600000000060000000001, ...
7 |
8 | 73, 6481, 64008001, 64000008000001, ...
9 | 8191, 81009001, 810000000000000000900000000000000001, ...

Numbers k such that b^2*10^(2*k) + b*10^k + 1 are prime: A297422 (b=2), A306751 (b=3), A308449 (b=5), A309582 (b=6), A309719 (b=8), A309744 (b=9).

Cf. A309739.

A296444 Numbers k such that 210^(2k) + 210^k + 1 are prime.

Original entry on oeis.org

0, 2, 3, 6, 10, 276, 746, 1090, 1485, 6186, 8571, 15594

Offset: 1

Patrick A. Thomas, Dec 13 2017

Numbers of this form divide 4*10^(4k)+1.

a(13) > 20000. - Michael S. Branicky, May 01 2025

			5, 20201, 2002001, 2000002000001, and 200000000020000000001 are prime, while 221=13*17, 200020001=569*351529, and 20000200001=17*29*1129*35933.

See A296443 for 2*10^(2k)-2*10^k+1.

Cf. A297422, A309739.

ParallelMap[ If[ PrimeQ[2*10^(2 #) + 2*10^# + 1], #, Nothing] &, Range@ 6500] (* Robert G. Wilson v, Dec 13 2017 *)

isok(k) = isprime(2*10^(2*k)+2*10^k+1); \\ Michel Marcus, Dec 13 2017

a(6)-a(7) from Michel Marcus, Dec 13 2017
a(8)-a(10) from Robert G. Wilson v, Dec 13 2017
a(1) = 0 inserted by Seiichi Manyama, Aug 15 2019
a(11) from Michael S. Branicky, Apr 16 2023
a(12) from Michael S. Branicky, Apr 30 2025

cp's OEIS Frontend

A309738 Primes of the form b^210^(2k) + b*10^k + 1 for 1 <= b <= 9, k >= 0.

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A296444 Numbers k such that 210^(2k) + 210^k + 1 are prime.

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cp's OEIS Frontend

A309738 Primes of the form b^2*10^(2*k) + b*10^k + 1 for 1 <= b <= 9, k >= 0.

Views

Author

Keywords

Examples

Crossrefs

A296444 Numbers k such that 2*10^(2k) + 2*10^k + 1 are prime.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

PARI

Extensions

A309738 Primes of the form b^210^(2k) + b*10^k + 1 for 1 <= b <= 9, k >= 0.

A296444 Numbers k such that 210^(2k) + 210^k + 1 are prime.