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.

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A275978 Numbers k such that (101*10^k + 1)/3 is prime.

Original entry on oeis.org

1, 4, 6, 12, 34, 54, 60, 61, 73, 148, 349, 552, 649, 967, 1044, 2521, 4501, 5721, 6133, 9052, 9880, 16126, 16215, 19146, 61770
Offset: 1

Views

Author

Robert Price, Aug 15 2016

Keywords

Comments

Numbers k such that the digits 33 followed by k-1 occurrences of the digit 6 followed by the digit 7 is prime (see Example section).
a(26) > 10^5.

Examples

			4 is in this sequence because (101*10^4 + 1)/3 = 336667 is prime.
Initial terms and associated primes:
a(1) = 1, 337;
a(2) = 4, 336667;
a(3) = 6, 33666667;
a(4) = 12, 33666666666667;
a(5) = 34, 336666666666666666666666666666666667, etc.

Links

Crossrefs

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[(101*10^# + 1)/3] &]
  • PARI
    isok(n) = isprime((101*10^n + 1)/3); \\ Michel Marcus, Aug 16 2016

A276046 Numbers k such that (26*10^k - 23)/3 is prime.

Original entry on oeis.org

1, 2, 10, 16, 78, 97, 125, 138, 192, 242, 290, 373, 408, 467, 583, 892, 899, 1709, 1944, 2154, 3618, 5225, 8974, 9377, 12504, 20042, 49106, 63073, 92152, 147973
Offset: 1

Views

Author

Robert Price, Aug 17 2016

Keywords

Comments

For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 6 followed by the digits 59 is prime (see Example section).
a(31) > 2*10^5.

Examples

			2 is in this sequence because (26*10^2 - 23)/3 = 859 is prime.
Initial terms and associated primes:
a(1) = 1, 79;
a(2) = 2, 859;
a(3) = 10, 86666666659;
a(4) = 16, 86666666666666659, etc.

Links

Crossrefs

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[(26*10^# - 23)/3] &]
  • PARI
    is(n)=ispseudoprime((26*10^n - 23)/3) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(30) from Robert Price, Dec 19 2019

A276047 Numbers k such that 4*10^k + 21 is prime.

Original entry on oeis.org

1, 2, 3, 7, 15, 22, 30, 35, 44, 73, 89, 91, 224, 533, 821, 1037, 1338, 1458, 1777, 2046, 2257, 2877, 3047, 3407, 13398, 42766, 55906, 61625, 66653, 123113, 229836, 238163
Offset: 1

Views

Author

Robert Price, Aug 17 2016

Keywords

Comments

For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 0 followed by the digits 21 is prime (see Example section).
a(33) > 3*10^5.

Examples

			3 is in this sequence because 4*10^3 + 21 = 4021 is prime.
Initial terms and associated primes:
a(1) = 1, 61;
a(2) = 2, 421;
a(3) = 3, 4021;
a(4) = 7, 40000021;
a(5) = 15, 4000000000000021, etc.

Links

Crossrefs

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[4*10^# + 21] &]
  • PARI
    is(n)=ispseudoprime(4*10^n + 21) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(30) from Robert Price, Dec 09 2018
a(31) - a(32) from Robert Price, Jun 01 2023

A276114 Numbers k such that (101*10^k - 17)/3 is prime.

Original entry on oeis.org

1, 2, 15, 17, 26, 41, 56, 59, 121, 137, 224, 506, 611, 836, 937, 1079, 1829, 2315, 2666, 2879, 6661, 7167, 14021, 15459, 32924, 73346, 176815, 177302
Offset: 1

Views

Author

Robert Price, Aug 18 2016

Keywords

Comments

Numbers k such that the digits 33 followed by k-1 occurrences of the digit 6 followed by the digit 1 is prime (see Example section).
a(29) > 2*10^5.

Examples

			2 is in this sequence because (101*10^2 - 17)/3 = 3361 is prime.
Initial terms and associated primes:
a(1) = 1, 331;
a(2) = 2, 3361;
a(3) = 15, 33666666666666661;
a(4) = 17, 3366666666666666661;
a(5) = 26, 3366666666666666666666666661, etc.

Links

Crossrefs

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[(101*10^# - 17)/3] &]
  • PARI
    is(n)=ispseudoprime((101*10^n  - 17)/3) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(27)-a(28) from Robert Price, Feb 05 2020

A276118 Numbers k such that 42 * 10^k + 1 is prime.

Original entry on oeis.org

0, 1, 2, 4, 13, 19, 39, 62, 76, 79, 109, 184, 222, 265, 370, 626, 670, 679, 763, 1950, 2174, 3379, 7369, 9087, 34990, 47535, 97970
Offset: 1

Views

Author

Robert Price, Aug 20 2016

Keywords

Comments

For k > 0, numbers k such that the digits 42 followed by k - 1 occurrences of the digit 0 followed by the digit 1 is prime (see the Example section).
a(28) > 10^5.

Examples

			4 is in this sequence because 42*10^4+1 = 420001 is prime.
Initial terms and associated primes:
a(1) = 0, 43;
a(2) = 1, 421;
a(3) = 2, 4201;
a(4) = 4, 420001;
a(5) = 13, 420000000000001, etc.

Links

Crossrefs

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[42 * 10^# + 1] &]
  • PARI
    is(n)=ispseudoprime(42*10^n+1) \\ Charles R Greathouse IV, Jun 13 2017

A276311 Numbers k such that (13*10^k + 197)/3 is prime.

Original entry on oeis.org

1, 2, 4, 5, 17, 21, 23, 28, 41, 43, 51, 59, 105, 115, 131, 273, 585, 1519, 2303, 4791, 4921, 6019, 7833, 25711, 27319, 32497, 37975, 49381, 87199
Offset: 1

Views

Author

Robert Price, Aug 29 2016

Keywords

Comments

For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 3 followed by the digits 99 is prime (see the Example section).
a(30) > 10^5.

Examples

			4 is in this sequence because (13*10^4 + 197)/3 = 43399 is prime.
Initial terms and associated primes:
a(1) = 1, 109;
a(2) = 2, 499;
a(3) = 4, 43399;
a(4) = 5, 433399;
a(5) = 17, 433333333333333399, etc.

Links

Crossrefs

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[(13*10^# + 197)/3] &]
  • PARI
    is(n)=ispseudoprime((13*10^n+197)/3) \\ Charles R Greathouse IV, Jun 13 2017

A276322 Numbers k such that (13*10^k + 83) / 3 is prime.

Original entry on oeis.org

1, 2, 5, 7, 17, 18, 25, 60, 64, 66, 118, 125, 1021, 1901, 2273, 2524, 6048, 7098, 8281, 11634, 13843, 16098, 18652, 18661, 20570, 32291, 34181, 59928, 65297, 86546
Offset: 1

Views

Author

Robert Price, Sep 01 2016

Keywords

Comments

For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 3 followed by the digits 61 is prime (see Example section).
a(31) > 2*10^5.

Examples

			5 is in this sequence because (13*10^5 + 83) / 3 = 433361 is prime.
Initial terms and associated primes:
a(1) = 1, 71;
a(2) = 2, 461;
a(3) = 5, 433361;
a(4) = 7, 43333361;
a(5) = 17, 433333333333333361, etc.

Links

Crossrefs

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[(13*10^# + 83) / 3] &]
  • PARI
    is(n)=ispseudoprime((13*10^n + 83)/3) \\ Charles R Greathouse IV, Jun 13 2017

A276353 Numbers k such that (19*10^k + 77) / 3 is prime.

Original entry on oeis.org

1, 2, 3, 5, 6, 17, 22, 56, 71, 90, 93, 109, 124, 135, 179, 255, 1804, 2541, 2707, 3195, 4952, 5884, 9301, 19847, 27903, 45739, 65545, 69424, 103907, 160619, 168173, 297497, 299640
Offset: 1

Views

Author

Robert Price, Aug 31 2016

Keywords

Comments

For k > 1, numbers k such that the digit 6 followed by k-2 occurrences of the digit 3 followed by the digits 59 is prime (see Example section).
a(34) > 3*10^5.

Examples

			3 is in this sequence because (19*10^3 + 77) / 3 = 6359 is prime.
Initial terms and associated primes:
a(1) = 1, 89;
a(2) = 2, 659
a(3) = 3, 6359;
a(4) = 5, 633359;
a(5) = 6, 6333359, etc.

Links

Crossrefs

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[(19*10^# + 77) / 3] &]
  • PARI
    is(n)=ispseudoprime((19*10^n + 77)/3) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(29)-a(31) from Robert Price, May 28 2019
a(32)-a(33) from Robert Price, Jun 01 2023

A276470 Numbers k such that (25*10^k + 167) / 3 is prime.

Original entry on oeis.org

1, 3, 4, 5, 11, 15, 18, 37, 41, 58, 60, 87, 117, 118, 214, 265, 334, 355, 450, 655, 1695, 1734, 2183, 3913, 25313, 32865
Offset: 1

Views

Author

Robert Price, Sep 12 2016

Keywords

Comments

For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 3 followed by the digits 89 is prime (see Example section).
a(27) > 2*10^5.

Examples

			3 is in this sequence because (25*10^3 + 167) / 3 = 8389 is prime.
Initial terms and associated primes:
a(1) = 1, 139;
a(2) = 3, 8389
a(3) = 4, 83389;
a(4) = 5, 833389;
a(5) = 11, 833333333389, etc.

Links

Crossrefs

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

Programs

  • Magma
    [n: n in [0..400] |IsPrime((25*10^n + 167) div 3)]; // Vincenzo Librandi, Sep 13 2016
  • Mathematica
    Select[Range[0, 100000], PrimeQ[(25*10^# + 167) / 3] &]
  • PARI
    is(n)=ispseudoprime((25*10^n + 167)/3) \\ Charles R Greathouse IV, Jun 13 2017

A276492 Numbers k such that 5*10^k + 59 is prime.

Original entry on oeis.org

1, 3, 7, 9, 10, 19, 21, 22, 43, 46, 58, 87, 216, 549, 604, 1147, 1858, 2952, 3684, 4057, 4246, 4354, 8212, 8289, 9013, 16968, 19107, 57754, 61348, 88254
Offset: 1

Views

Author

Robert Price, Sep 05 2016

Keywords

Comments

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 0 followed by the digits 59 is prime (see Example section).
a(31) > 2*10^5.

Examples

			3 is in this sequence because 5*10^3 + 59 = 5059 is prime.
Initial terms and associated primes:
a(1) = 1, 109;
a(2) = 3, 5059;
a(3) = 7, 50000059;
a(4) = 9, 5000000059;
a(5) = 10, 50000000059, etc.

Links

Crossrefs

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[5*10^# + 59] &]
  • PARI
    is(n)=ispseudoprime(5*10^n + 59) \\ Charles R Greathouse IV, Jun 13 2017
Previous Showing 91-100 of 490 results. Next

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