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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A286395 Numbers k such that (17*10^k + 67)/3 is prime.

Original entry on oeis.org

1, 3, 7, 8, 9, 11, 15, 19, 29, 55, 76, 159, 266, 311, 394, 908, 1732, 1875, 4335, 6334, 7641, 16421, 33721, 139239, 157705, 160143
Offset: 1

Views

Author

Robert Price, May 09 2017

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 89 is prime (see Example section).
a(27) > 2*10^5.

Examples

			3 is in this sequence because (17*10^3 + 67)/3 = 5689 is prime.
Initial terms and associated primes:
a(1) = 1, 79;
a(2) = 3, 5689;
a(3) = 7, 56666689;
a(4) = 8, 566666689;
a(5) = 9, 5666666689; etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[(17*10^# + 67)/3] &]

Extensions

a(24)-a(26) from Robert Price, Jan 24 2019

A289051 Numbers k such that 13*10^k + 1 is prime.

Original entry on oeis.org

1, 2, 3, 7, 16, 53, 95, 105, 125, 163, 358, 423, 562, 1774, 3459, 13957, 17962, 51179, 65963, 72808
Offset: 1

Views

Author

Robert Price, Jun 22 2017

Keywords

Comments

For k > 0, numbers k such that the digits 13 followed by k-1 occurrences of the digit 0 followed by the digit 1 is prime (see Example section).
a(21) > 10^5.

Examples

			2 is in this sequence because 13*10^3 + 1 = 1301 is prime.
Initial terms and associated primes:
a(1) = 1, 131;
a(2) = 2, 1301;
a(3) = 3, 13001;
a(4) = 7, 130000001;
a(5) = 16, 130000000000000001; etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[13*10^# + 1] &]

A290962 Numbers k such that (13*10^k - 43)/3 is prime.

Original entry on oeis.org

1, 2, 4, 5, 8, 12, 55, 125, 136, 221, 224, 668, 1254, 2639, 4745, 5888, 8526, 9139, 13771, 17936, 27713, 38668, 44680, 73891, 135184, 200610, 215592, 247793, 258710, 291721
Offset: 1

Views

Author

Robert Price, Aug 15 2017

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 19 is prime (see Example section).
a(31) > 3*10^5.

Examples

			2 is in this sequence because (13*10^2 - 43)/3 = 419 is prime.
Initial terms and associated primes:
a(1) = 1, 29;
a(2) = 2, 419;
a(3) = 4, 43319;
a(4) = 5; 433319;
a(5) = 8, 433333319; etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[1, 100000], PrimeQ[(13*10^# - 43)/3] &]
  • PARI
    isok(n) = ispseudoprime((13*10^n - 43)/3) \\ Altug Alkan, Aug 15 2017

Extensions

a(25) from Robert Price, Nov 28 2018
a(26)-a(30) from Robert Price, Oct 26 2023

A290964 Numbers k such that (35*10^k - 593)/9 is prime.

Original entry on oeis.org

3, 5, 6, 14, 24, 84, 87, 207, 734, 797, 1743, 2211, 3539, 5871, 5949, 6954, 8309, 10896, 12771, 22382, 35112, 38267, 69866, 121229, 125754, 133979
Offset: 1

Views

Author

Robert Price, Aug 15 2017

Keywords

Comments

For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 8 followed by the digits 23 is prime (see Example section).
a(27) > 2*10^5.

Examples

			5 is in this sequence because (35*10^5 - 593)/9 = 388823 is prime.
Initial terms and associated primes:
a(1) = 3, 3823;
a(2) = 5, 388823;
a(3) = 6, 3888823;
a(4) = 14; 388888888888823;
a(5) = 24, 3888888888888888888888823; etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[2, 100000], PrimeQ[(35*10^# - 593)/9] &]
  • PARI
    isok(n) = ispseudoprime((35*10^n - 593)/9) \\ Altug Alkan, Aug 15 2017

Extensions

a(24)-a(26) from Robert Price, Jul 18 2018

A291609 Numbers k such that (49*10^k - 67)/9 is prime.

Original entry on oeis.org

1, 3, 4, 7, 10, 24, 37, 46, 63, 64, 91, 114, 367, 453, 1156, 1347, 1524, 7153, 10893, 13548, 15153, 43093, 61167, 184993
Offset: 1

Views

Author

Robert Price, Aug 27 2017

Keywords

Comments

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 4 followed by the digits 37 is prime (see Example section).
a(25) > 2*10^5.

Examples

			4 is in this sequence because (49*10^4 - 67)/9 = 54437 is prime.
Initial terms and associated primes:
a(1) = 1, 47;
a(2) = 3, 5437;
a(3) = 4, 54437;
a(4) = 7, 54444437;
a(5) = 10, 54444444437; etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[1, 100000], PrimeQ[(49*10^# - 67)/9] &]

Extensions

a(24) from Robert Price, Mar 15 2019

A291611 Numbers k such that 5*10^k + 81 is prime.

Original entry on oeis.org

1, 3, 6, 16, 30, 33, 36, 37, 85, 288, 561, 805, 850, 1057, 1192, 1312, 2571, 4579, 5223, 5940, 10191, 18756, 24564, 29595, 43891, 65905, 89118, 97963, 112003, 139945, 174101, 195221
Offset: 1

Views

Author

Robert Price, Aug 27 2017

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 81 is prime (see Example section).
a(33) > 2*10^5.

Examples

			3 is in this sequence because 5*10^3 + 81 = 5081 is prime.
Initial terms and associated primes:
a(1) = 1, 131;
a(2) = 3, 5081;
a(3) = 6, 5000081;
a(4) = 16, 50000000000000081;
a(5) = 30, 5000000000000000000000000000081; etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[5*10^# + 81] &]

Extensions

a(29)-a(32) from Robert Price, Mar 04 2019
Terms reordered into ascending order by Robert Price, Apr 03 2022

A295325 Numbers k such that 15*10^k + 1 is prime.

Original entry on oeis.org

1, 4, 7, 8, 18, 19, 73, 143, 192, 408, 533, 792, 3179, 7709, 9554, 35598, 41587, 52919, 56021, 61604, 78672, 81624
Offset: 1

Views

Author

Robert Price, Nov 19 2017

Keywords

Comments

For k > 1, numbers k such that the digits 15 followed by k-1 occurrences of the digit 0 followed by the digit 1 is prime (see Example section).
a(23) > 10^5.

Examples

			4 is in this sequence because 15*10^4 + 1 = 150001 is prime.
Initial terms and associated primes:
a(1) = 1, 151;
a(2) = 4, 150001;
a(3) = 7, 150000001;
a(4) = 8, 1500000001;
a(5) = 18, 15000000000000000001; etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[15*10^# + 1] &]
  • PARI
    isok(k) = isprime(15*10^k + 1); \\ Michel Marcus, Nov 20 2017

A102740 Numbers k such that 7*10^k - 11 is prime.

Original entry on oeis.org

1, 6, 7, 9, 10, 11, 16, 42, 53, 78, 321, 699, 1858, 3425, 4899, 5734, 11081, 11675, 12136, 14056, 16074, 77969, 158465
Offset: 1

Views

Author

Tom Mueller (muel4503(AT)uni-trier.de), Feb 08 2005

Keywords

Comments

a(24) > 2*10^5.
Numbers corresponding to terms <= 699 are certified primes. - Klaus Brockhaus, Feb 15 2005
For k > 1, numbers k such that the digit 6 followed by k-2 occurrences of the digit 9 followed by the digits 89 is prime (see Example section).

Examples

			Initial terms and associated primes:
a(1) = 1, 59;
a(2) = 6, 6999989;
a(3) = 7, 69999989;
a(4) = 9, 6999999989;
a(5) = 10, 69999999989; etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[1, 100000], PrimeQ[7*10^# - 11] &]
  • PARI
    is(n)=ispseudoprime(7*10^n - 11) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(11)-a(13) from Klaus Brockhaus, Feb 15 2005
a(14)-a(22) from Robert Price, Oct 29 2017
a(23) from Robert Price, Jun 21 2019

A256228 Numbers k such that 4*10^k - 21 is prime.

Original entry on oeis.org

1, 2, 4, 5, 7, 9, 10, 17, 21, 41, 51, 59, 61, 77, 79, 83, 97, 108, 427, 615, 869, 900, 966, 3150, 3239, 3932, 5218, 11941, 30558, 44697, 90334, 113874, 128343, 142810, 222253
Offset: 1

Views

Author

Robert Price, Apr 17 2016

Keywords

Comments

For k > 1, numbers that begin with the digit 3 followed by k-2 occurrences of the digit 9 followed by the digits 79 are prime (see Example section).
a(36) > 3*10^5.

Examples

			4 is in this sequence because 4*10^4 - 21 = 39979, which is prime.
Initial terms and associated primes:
a(1) = 1, 19;
a(2) = 2, 379;
a(3) = 4, 39979;
a(4) = 5, 399979;
a(5) = 7, 39999979, etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[1, 100000], PrimeQ[4*10^# - 21] &]
  • PARI
    is(n)=ispseudoprime(4*10^n - 21) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(32)-a(34) from Robert Price, Sep 10 2018
a(35) from Robert Price, Jun 01 2023

A257027 Numbers k such that 7*R_(k+2) - 6*10^k is prime, where R_k = 11...1 is the repunit (A002275) of length k.

Original entry on oeis.org

0, 2, 3, 9, 11, 18, 74, 131, 144, 161, 224, 282, 390, 398, 614, 791, 1313, 1866, 9708, 10544, 13292, 13394, 29703, 30779, 72446
Offset: 1

Views

Author

Robert Price, Apr 14 2015

Keywords

Comments

Also, numbers k such that (646*10^k - 7)/9 is prime.
Terms from Kamada.
a(26) > 10^5. Robert Price, Jul 31 2016

Examples

			For k=2, 7*R_4 - 6*10^2 = 7777 - 600 = 7177 which is prime.
a(1)=0 associated with 71, a(2)=2 associated with 7177, a(3)=3 associated with 71777, a(4)=9 associated with 71777777777, etc. - _Robert Price_, Jul 31 2016

Links

Crossrefs

Cf. A002275, A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

Programs

  • Magma
    [n: n in [0..300] | IsPrime((646*10^n-7) div 9)]; // Vincenzo Librandi, Apr 15 2015
  • Mathematica
    Select[Range[0, 100000], PrimeQ[(646*10^#-7)/9 ] &]
  • PARI
    for(n=0,200,if(isprime((646*10^n-7)/9),print1(n,", "))) \\ Derek Orr, Apr 14 2015

Extensions

a(25) from Robert Price, Jul 31 2016
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