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 1-6 of 6 results.

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

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Aug 15 2019

Keywords

Examples

			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, ...
		

Crossrefs

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.

A306751 Numbers k such that 9*10^(2*k) + 3*10^k + 1 is prime.

Original entry on oeis.org

0, 5, 14, 77, 104, 2603, 2657, 24029
Offset: 1

Views

Author

Seiichi Manyama, Aug 15 2019

Keywords

Examples

			         13 is prime ==> a(1) = 0.
        931 = 7^2 * 19.
      90301 = 73 * 1237.
    9003001 = 7 * 757 * 1699.
  900030001 = 13 * 4969 * 13933.
90000300001 is prime ==> a(2) = 5.
		

Crossrefs

Programs

  • PARI
    for(k=0, 1e3, if(ispseudoprime(9*100^k+3*10^k+1), print1(k", ")))

Extensions

a(8) from Michael S. Branicky, Sep 05 2024

A308449 Numbers k such that 25*10^(2*k) + 5*10^k + 1 are prime.

Original entry on oeis.org

0, 1, 2, 14, 174, 448, 16562
Offset: 1

Views

Author

Seiichi Manyama, Aug 15 2019

Keywords

Examples

			          31 is prime ==> a(1) = 0.
        2551 is prime ==> a(2) = 1.
      250501 is prime ==> a(3) = 2.
    25005001 = 7 * 79 * 103 * 439.
  2500050001 = 19 * 2269 * 57991.
250000500001 = 7 * 103561 * 344863.
		

Crossrefs

Cf. A309738.

Programs

  • PARI
    for(k=0, 1e3, if(ispseudoprime(25*100^k+5*10^k+1), print1(k", ")))

Extensions

a(7) from Michael S. Branicky, Apr 17 2023

A309582 Numbers k such that 36*10^(2*k) + 6*10^k + 1 is prime.

Original entry on oeis.org

0, 10, 118, 138, 1143, 16344, 19324
Offset: 1

Views

Author

Seiichi Manyama, Aug 15 2019

Keywords

Comments

a(6) > 6000. - Tyler NeSmith, Dec 05 2021

Examples

			                    43 is prime ==> a(1) = 0.
                  3661 = 7 * 523.
                360601 = 19 * 18979.
              36006001 = 67 * 537403.
            3600060001 = 457 * 7877593.
          360000600001 = 7 * 51428657143.
        36000006000001 = 379 * 94986823219.
      3600000060000001 = 7 * 43 * 64609 * 185115589.
    360000000600000001 = 19 * 18947368452631579.
  36000000006000000001 = 307 * 1249 * 1071121 * 87652267.
3600000000060000000001 is prime ==> a(2) = 10.
		

Crossrefs

Cf. A309738.

Programs

  • PARI
    for(k=0, 1e3, if(ispseudoprime(36*100^k+6*10^k+1), print1(k", ")))

Extensions

a(6) from Michael S. Branicky, Apr 24 2023
a(7) from Michael S. Branicky, Sep 07 2024

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

Original entry on oeis.org

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

Views

Author

Seiichi Manyama, Aug 15 2019

Keywords

Examples

			            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.
		

Crossrefs

Programs

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

Extensions

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

A309744 Numbers k such that 81*10^(2*k) + 9*10^k + 1 is prime.

Original entry on oeis.org

1, 3, 17, 31, 7101, 14183
Offset: 1

Views

Author

Seiichi Manyama, Aug 15 2019

Keywords

Examples

			                  91 = 7 * 13.
                8191 is prime ==> a(1) = 0.
              810901 = 7^2 * 13 * 19 * 67.
            81009001 is prime ==> a(2) = 3.
          8100090001 = 73 * 271 * 331 * 1237.
        810000900001 = 1471 * 550646431.
      81000009000001 = 7 * 13 * 613 * 757 * 1129 * 1699.
    8100000090000001 = 31 * 439 * 595194363289.
  810000000900000001 = 7 * 13 * 157 * 193 * 4243 * 4969 * 13933.
81000000009000000001 = 271 * 298892988963099631.
		

Crossrefs

Programs

  • PARI
    for(k=0, 1e3, if(ispseudoprime(81*100^k+9*10^k+1), print1(k", ")))

Extensions

a(6) from Michael S. Branicky, Sep 05 2024
Showing 1-6 of 6 results.