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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A273679 Numbers k such that 10^k - 1000000001 is prime.

Original entry on oeis.org

11, 18, 22, 26, 27, 36, 45, 59, 140, 162, 201, 278, 427, 563, 588, 757, 951, 2006, 3938, 4127, 4490, 5637, 6074, 6725, 7025, 10191, 25628, 39415, 51872, 57501, 90227, 115773, 117142, 148934
Offset: 1

Views

Author

Robert Price, May 27 2016

Keywords

Comments

For k > 9, numbers k such that k-10 occurrences of the digit 9 followed by the digits 8999999999 is prime (see Example section).
a(35) > 2*10^5.

Examples

			11 is in this sequence because 10^11 - 1000000001 = 98999999999 is prime.
Initial terms and associated primes:
a(1) = 11, 98999999999,
a(2) = 18, 999999998999999999,
a(3) = 22, 9999999999998999999999,
a(4) = 26, 99999999999999998999999999,
a(5) = 27, 999999999999999998999999999, etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[10^#-1000000001] &]
  • PARI
    is(n)=ispseudoprime(10^n-10^9-1) \\ Charles R Greathouse IV, Jun 08 2016
  • Python
    from sympy import isprime
def afind(limit):
    tenk = 10**10
    for k in range(10, limit+1):
        if isprime(tenk - 1000000001): print(k, end=", ")
        tenk *= 10
afind(100000) # Michael S. Branicky, Nov 18 2021

Extensions

a(32)-a(33) from Robert Price, Mar 01 2018
a(34) from Robert Price, Dec 31 2020

A273726 Numbers k such that (25*10^k + 59)/3 is prime.

Original entry on oeis.org

1, 2, 3, 5, 7, 26, 52, 75, 97, 98, 160, 227, 295, 413, 686, 901, 975, 1088, 1481, 2555, 4001, 4361, 5637, 7568, 8641, 19526, 26633, 92186
Offset: 1

Views

Author

Robert Price, May 28 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 53 is prime (see Example section).
a(29) > 2*10^5.

Examples

			3 is in this sequence because (25*10^3+59)/3 = 8353 is prime.
Initial terms and associated primes:
a(1) = 1, 103;
a(2) = 2, 853;
a(3) = 3, 8353;
a(4) = 5, 833353;
a(5) = 6, 83333353, etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[(25*10^# + 59)/3] &]
  • PARI
    is(n)=ispseudoprime((25*10^n + 59)/3) \\ Charles R Greathouse IV, Jun 08 2016

A273728 Numbers k such that (17*10^k + 79)/3 is prime.

Original entry on oeis.org

1, 2, 3, 5, 7, 12, 37, 45, 55, 139, 205, 264, 445, 975, 1111, 1298, 1340, 1835, 2264, 2317, 2897, 2955, 3001, 4134, 6637, 7063, 20613, 114795, 147890
Offset: 1

Views

Author

Robert Price, May 28 2016

Keywords

Comments

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 6 followed by the digits 93 is prime (see Example section).
a(30) > 3*10^5. - Robert Price, Jul 10 2023

Examples

			3 is in this sequence because (17*10^3+79)/3 = 5693 is prime.
Initial terms and associated primes:
a(1) = 1, 83;
a(2) = 2, 593;
a(3) = 3, 5693;
a(4) = 5, 566693;
a(5) = 7, 56666693, etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[(17*10^# + 79)/3] &]
  • PARI
    is(n)=ispseudoprime((17*10^n + 79)/3) \\ Charles R Greathouse IV, Jun 08 2016

Extensions

a(28)-a(29) from Robert Price, Apr 15 2019

A273783 Numbers k such that (86*10^k - 77)/9 is prime.

Original entry on oeis.org

2, 3, 8, 9, 12, 14, 27, 32, 50, 80, 98, 99, 194, 237, 338, 828, 830, 1265, 2583, 3639, 5232, 5940, 9371, 10268, 13424, 26975, 36147, 60165, 69260, 93263
Offset: 1

Views

Author

Robert Price, May 30 2016

Keywords

Comments

For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 5 followed by the digits 47 is prime (see Example section).
a(31) > 2*10^5.

Examples

			3 is in this sequence because (86*10^3 - 77)/9 = 9547 is prime.
Initial terms and associated primes:
a(1) = 2, 947;
a(2) = 3, 9547;
a(3) = 8, 955555547;
a(4) = 9, 9555555547;
a(5) = 12, 9555555555547, etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[(86*10^# - 77)/9] &]
  • PARI
    is(n)=ispseudoprime((86*10^n - 77)/9) \\ Charles R Greathouse IV, Jun 08 2016

A273907 Numbers k such that 2*10^k - 87 is prime.

Original entry on oeis.org

2, 3, 4, 9, 10, 13, 15, 24, 26, 38, 39, 42, 433, 489, 495, 513, 597, 829, 2019, 2738, 3096, 3691, 5437, 7537, 8536, 34125, 40105, 41790, 52713, 104811, 173809, 175860
Offset: 1

Views

Author

Robert Price, Jun 03 2016

Keywords

Comments

For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 9 followed by the digits 13 is prime (see Example section).
a(33) > 2*10^5.

Examples

			3 is in this sequence because 2*10^3 - 87 = 1913 is prime.
Initial terms and associated primes:
a(1) = 2, 113;
a(2) = 3, 1913;
a(3) = 4, 19913;
a(4) = 9, 1999999913;
a(5) = 10, 19999999913, etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[2*10^# - 87] &]
  • PARI
    is(n)=ispseudoprime(2*10^n - 87) \\ Charles R Greathouse IV, Jun 08 2016

Extensions

a(30)-a(32) from Robert Price, Apr 13 2018

A273924 Numbers k such that (7*10^k - 13)/3 is prime.

Original entry on oeis.org

1, 2, 5, 6, 28, 53, 56, 86, 88, 90, 96, 136, 142, 186, 202, 373, 448, 785, 988, 1263, 1966, 3561, 4768, 9658, 9831, 17797, 42286, 49893, 98007, 129472, 146860
Offset: 1

Views

Author

Robert Price, Jun 04 2016

Keywords

Comments

For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 3 followed by the digits 29 is prime (see Example section).
a(32) > 2*10^5.

Examples

			5 is in this sequence because (7*10^5 - 13)/3 = 233329 is prime.
Initial terms and associated primes:
a(1) = 1, 19;
a(2) = 2, 229;
a(3) = 5, 233329;
a(4) = 6, 2333329;
a(5) = 28, 23333333333333333333333333329, etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[(7*10^# - 13)/3] &]
  • PARI
    is(n)=ispseudoprime((7*10^n - 13)/3) \\ Charles R Greathouse IV, Jun 08 2016

Extensions

a(30)-a(31) from Robert Price, Jul 13 2018

A273944 Numbers k such that (266*10^k - 17)/3 is prime.

Original entry on oeis.org

0, 1, 2, 3, 7, 8, 11, 14, 24, 29, 50, 78, 99, 192, 226, 519, 613, 651, 1492, 3720, 6567, 6791, 7226, 8471, 9050, 13521, 14255, 33529, 44072, 47844, 64102, 112930, 116024, 122872, 138328, 140681, 268407
Offset: 1

Views

Author

Robert Price, Jun 17 2016

Keywords

Comments

For k > 1, numbers k such that the digits 88 followed by k-1 occurrences of the digit 6 followed by the digit 1 is prime (see Example section).
a(38) > 3*10^5.

Examples

			3 is in this sequence because (266*10^3-17)/3 = 88661 is prime.
Initial terms and associated primes:
a(1) = 0, 83;
a(2) = 1, 881;
a(3) = 2, 8861;
a(4) = 3, 88661;
a(5) = 7, 886666661, etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[(266*10^# - 17)/3] &]
  • PARI
    isok(n) = isprime((266*10^n - 17)/3); \\ Michel Marcus, Jun 18 2016

Extensions

a(32)-a(36) from Robert Price, Jul 16 2020
a(37) from Robert Price, Jun 21 2023

A274037 Numbers k such that 3*10^k - 49 is prime.

Original entry on oeis.org

2, 5, 6, 10, 16, 29, 35, 82, 107, 170, 185, 204, 223, 226, 388, 512, 1586, 2137, 3182, 7325, 7346, 8143, 8746, 11322, 11497, 13279, 44681, 108624, 183872
Offset: 1

Views

Author

Robert Price, Jun 07 2016

Keywords

Comments

For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 9 followed by the digits 51 is prime (see Example section).
a(31) > 2*10^5.

Examples

			5 is in this sequence because 3*10^5-49 = 299951 is prime.
Initial terms and associated primes:
a(1) = 2, 251;
a(2) = 5, 299951;
a(3) = 6, 2999951;
a(4) = 10, 29999999951;
a(5) = 16, 29999999999999951, etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[3*10^# - 49] &]
  • PARI
    is(n)=ispseudoprime(3*10^n - 49) \\ Charles R Greathouse IV, Jun 08 2016

Extensions

a(28)-a(29) from Robert Price, Jul 29 2018

A274214 Numbers k such that 4*10^k + 63 is prime.

Original entry on oeis.org

0, 1, 2, 4, 6, 9, 11, 14, 16, 26, 54, 74, 111, 130, 152, 253, 345, 607, 686, 1590, 2711, 5462, 7021, 8681, 11044, 18132, 24072, 25211, 44332, 52792, 85881
Offset: 1

Views

Author

Robert Price, Jun 13 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 63 is prime (see Example section).
a(32) > 2*10^5.

Examples

			4 is in this sequence because 4*10^4 + 63 = 40063 is prime.
Initial terms and associated primes:
a(1) = 0, 67;
a(2) = 1, 103;
a(3) = 2, 463;
a(4) = 4, 40063;
a(5) = 6, 4000063, etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[4*10^# + 63] &]
  • PARI
    is(n)=ispseudoprime(4*10^n + 63) \\ Charles R Greathouse IV, Jun 13 2017

A274238 Numbers k such that (26*10^k - 119)/3 is prime.

Original entry on oeis.org

1, 2, 3, 4, 6, 22, 25, 29, 59, 89, 221, 453, 535, 1708, 2242, 2413, 3581, 4234, 4848, 5380, 6548, 8654, 11035, 17308, 27634, 28807, 35481, 79678, 80875, 114658, 230394
Offset: 1

Views

Author

Robert Price, Jul 06 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 27 is prime (see Example section).
a(32) > 3*10^5.

Examples

			3 is in this sequence because (26*10^3 - 119)/3 = 8627 is prime.
Initial terms and associated primes:
a(1) = 1, 47;
a(2) = 2, 827;
a(3) = 3, 8627;
a(4) = 4, 86627;
a(5) = 6, 8666627, etc.

Links

Crossrefs

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

Programs

  • Magma
    [n: n in [1..500] |IsPrime((26*10^n-119) div 3)]; // Vincenzo Librandi, Jul 07 2016
  • Mathematica
    Select[Range[0, 100000], PrimeQ[(26*10^# - 119)/3] &]
  • PARI
    lista(nn) = for(n=1, nn, if(ispseudoprime((26*10^n-119)/3), print1(n, ", "))); \\ Altug Alkan, Jul 08 2016

Extensions

a(30)-a(31) from Robert Price, Jul 12 2023
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