A309742 -id:A309742 - cp's OEIS frontend

A309739 Primes of the form b10^(2k) + b*10^k + 1 for 1 <= b <= 9, k >= 0.

3, 5, 7, 11, 13, 17, 19, 331, 661, 881, 991, 20201, 60601, 90901, 2002001, 5005001, 300030001, 600060001, 50000500001, 2000002000001, 8000008000001, 9000009000001, 3000000003000000001, 200000000020000000001, 80000000000800000000001

Offset: 1

Seiichi Manyama, Aug 15 2019

			b | Primes of the form b*10^(2*k) + b*10^k + 1
--+-------------------------------------------------------------
1 | 3.
2 | 5, 20201, 2002001, 2000002000001, 200000000020000000001, ...
3 | 7, 331, 300030001, 3000000003000000001.
4 |
5 | 11, 5005001, 50000500001, ...
6 | 13, 661, 60601, 600060001, ...
7 |
8 | 17, 881, 8000008000001, 80000000000800000000001, ...
9 | 19, 991, 90901, 9000009000001, 9000000000009000000000001, ...

Numbers k such that b*10^(2*k) + b*10^k + 1 are prime: A296444 (b=2), A309740 (b=5), A309741 (b=6), A309742 (b=8), A309743 (b=9).
Primes of the form b*10^(2*k) + b*10^k + 1: A160432 (b=3).
Cf. A309738.

A309719 Numbers k such that 6410^(2k) + 8*10^k + 1 is prime.

Original entry on oeis.org

0, 1, 3, 6, 12, 2555, 3281, 5292, 11209

Offset: 1

Seiichi Manyama, Aug 15 2019

			            73 is prime ==> a(1) = 0.
          6481 is prime ==> a(2) = 1.
        640801 = 7 * 31 * 2953.
      64008001 is prime ==> a(3) = 3.
    6400080001 = 7 * 13441 * 68023.
  640000800001 = 619 * 1033926979.
64000008000001 is prime ==> a(4) = 6.

Cf. A309738, A309742.

for(k=0, 1e3, if(ispseudoprime(64*100^k+8*10^k+1), print1(k", ")))

a(9) from Michael S. Branicky, Sep 04 2024

cp's OEIS Frontend

A309739 Primes of the form b10^(2k) + b*10^k + 1 for 1 <= b <= 9, k >= 0.

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A309719 Numbers k such that 6410^(2k) + 8*10^k + 1 is prime.

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cp's OEIS Frontend

A309739 Primes of the form b*10^(2*k) + b*10^k + 1 for 1 <= b <= 9, k >= 0.

Views

Author

Keywords

Examples

Crossrefs

A309719 Numbers k such that 64*10^(2*k) + 8*10^k + 1 is prime.

Views

Author

Keywords

Examples

Crossrefs

Programs

PARI

Extensions

A309739 Primes of the form b10^(2k) + b*10^k + 1 for 1 <= b <= 9, k >= 0.

A309719 Numbers k such that 6410^(2k) + 8*10^k + 1 is prime.