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 1-10 of 507 results. Next

A268448 Numbers k such that (35*10^k - 11)/3 is prime.

Original entry on oeis.org

1, 2, 4, 5, 6, 7, 14, 21, 27, 34, 53, 72, 96, 145, 168, 191, 192, 309, 393, 502, 667, 1055, 1534, 1710, 4171, 4838, 4950, 9932, 10860, 11906, 14148, 17184, 27054, 31435
Offset: 1

Views

Author

Robert Price, Feb 04 2016

Keywords

Comments

Numbers k such that digits 11 followed by k-1 occurrences of digit 6 followed by digit 3 is prime. E.g., 116666...666663.
a(35) > 3*10^5. - Robert Price, Oct 16 2015

Examples

			7 is in this sequence because (35*10^7 - 11)/3 = 116666663 is prime.

Links

Crossrefs

Cf. A056654.

Programs

  • Magma
    [n: n in [0..400] |IsPrime((35*10^n-11) div 3)]; // Vincenzo Librandi, Feb 05 2016
  • Mathematica
    Select[Range[0, 100000], PrimeQ[(35*10^# - 11)/3] &]
  • PARI
    lista(nn) = {for(n=1, nn, if(ispseudoprime((35*10^n-11)/3), print1(n, ", ")));} \\ Altug Alkan, Feb 05 2016

A269303 Numbers k such that (266*10^k + 1)/3 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 8, 10, 13, 19, 26, 37, 69, 77, 81, 214, 242, 255, 900, 1113, 1833, 3166, 3566, 4753, 4849, 4869, 5005, 7372, 7702, 10240, 16100, 18972, 28574, 33815, 37820, 70457, 89482, 106066, 133603, 154897, 278325
Offset: 1

Views

Author

Robert Price, Feb 22 2016

Keywords

Comments

For k > 0, numbers k such that digits 88 followed by k-1 occurrences of digit 6 followed by the digit 7 is prime (see Example section).
a(43) > 3*10^5.

Examples

			6 is in this sequence because (266*10^n+1)/3 = 88666667 is prime.
Initial terms and associated primes:
a(1)  = 0,    89;
a(2)  = 1,    887;
a(3)  = 2,    8867;
a(4)  = 3,    88667;
a(5)  = 4,    886667;
a(6)  = 5,    8866667;
a(7)  = 6,    88666667;
a(8)  = 8,    8866666667;
a(9)  = 10,   886666666667;
a(10) = 13,   886666666666667, etc.

Links

Crossrefs

Cf. A056654, A268448.

Programs

  • Magma
    [n: n in [0..220] | IsPrime((266*10^n + 1) div 3)]; // Vincenzo Librandi, Feb 23 2016
  • Mathematica
    Select[Range[0, 100000], PrimeQ[(266*10^#+1)/3] &]
  • PARI
    is(n)=ispseudoprime((266*10^n + 1)/3) \\ Charles R Greathouse IV, Feb 16 2017

Extensions

a(39)-a(41) from Robert Price, Apr 22 2020
a(42) from Robert Price, May 31 2023

A270339 Numbers k such that (11*10^k + 19)/3 is prime.

Original entry on oeis.org

1, 2, 3, 9, 17, 18, 20, 24, 29, 36, 48, 114, 126, 135, 153, 170, 241, 363, 483, 579, 681, 948, 2483, 2798, 3081, 5137, 5640, 6890, 7080, 12600, 16929, 24253, 24793, 35546, 52956, 69645, 133831, 206688
Offset: 1

Views

Author

Robert Price, Mar 15 2016

Keywords

Comments

For k > 1, numbers k such that the digit 3 followed by k-2 occurrences of the digit 6 followed by the digits 73 is prime (see Example section).
a(39) > 3*10^5.

Examples

			3 is in this sequence because (11*10^3 + 19)/3 = 3673 is prime.
Initial terms and associated primes:
a(1) = 1, 43;
a(2) = 2, 373;
a(3) = 3, 3673;
a(4) = 9, 3666666673;
a(5) = 17, 366666666666666673, etc.

Links

Crossrefs

Cf. A056654, A268448, A269303.

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[(11*10^# + 19)/3] &]
  • PARI
    is(n)=isprime((11*10^n + 19)/3) \\ Charles R Greathouse IV, Mar 16 2016

Extensions

a(37) from Robert Price, Sep 16 2018
a(38) from Robert Price, Jul 25 2024

A270613 Numbers k such that (68*10^k + 7)/3 is prime.

Original entry on oeis.org

1, 2, 3, 4, 7, 10, 24, 25, 29, 34, 35, 37, 46, 49, 88, 103, 290, 381, 484, 696, 751, 886, 999, 1750, 5062, 6214, 9740, 12558, 16551, 24674, 28600, 37427, 48032, 61991, 70148, 72516, 99441, 179656
Offset: 1

Views

Author

Robert Price, Mar 20 2016

Keywords

Comments

Numbers k such that the digits 22 followed by k-1 occurrences of the digit 6 followed by the digit 9 is prime (see Example section).
a(39) > 3*10^5.

Examples

			3 is in this sequence because (68*10^3+7)/3 = 22669 is prime.
Initial terms and associated primes:
a(1) = 1, 229;
a(2) = 2, 2269;
a(3) = 3, 22669;
a(4) = 4, 226669;
a(5) = 7, 226666669, etc.

Links

Crossrefs

Cf. A056654, A268448, A269303, A270339.

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[(68*10^# + 7)/3] &]
  • PARI
    lista(nn) = for(n=1, nn, if(ispseudoprime((68*10^n + 7)/3), print1(n, ", "))); \\ Altug Alkan, Mar 20 2016

Extensions

a(38) from Robert Price, Jan 16 2020

A270831 Numbers k such that (7*10^k + 71)/3 is prime.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 23, 29, 37, 39, 40, 89, 115, 189, 227, 253, 301, 449, 533, 607, 969, 1036, 1207, 1407, 1701, 3493, 7147, 11342, 21638, 22327, 25575, 25648, 34079, 39974, 47719, 49913, 74729, 100737, 103531, 168067
Offset: 1

Views

Author

Robert Price, Mar 23 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 57 is prime (see Example section).
a(41) > 2*10^5.

Examples

			3 is in this sequence because (7*10^3 + 71)/3 = 2357 is prime.
Initial terms and associated primes:
a(1) = 1, 47;
a(2) = 2, 257;
a(3) = 3, 2357;
a(4) = 4, 23357;
a(5) = 5, 233357, etc.

Links

Crossrefs

Cf. A056654, A268448, A269303, A270339, A270613.

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[(7*10^# + 71)/3] &]
  • PARI
    lista(nn) = {for(n=1, nn, if(ispseudoprime((7*10^n + 71)/3), print1(n, ", "))); } \\ Altug Alkan, Mar 23 2016

Extensions

a(38)-a(40) from Robert Price, May 21 2018

A270890 Numbers k such that (8*10^k + 49)/3 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 10, 24, 33, 34, 35, 45, 52, 56, 62, 65, 103, 166, 424, 886, 1418, 1825, 4895, 5715, 7011, 7810, 9097, 12773, 14746, 20085, 25359, 27967, 46629, 48507, 68722, 74944, 102541, 118960, 157368
Offset: 1

Views

Author

Robert Price, Mar 25 2016

Keywords

Comments

For k > 2, numbers k such that the digit 2 followed by k-3 occurrences of the digit 6 followed by the digits 83 is prime (see Example section).
a(41) > 3*10^5.

Examples

			3 is in this sequence because (8*10^3 + 49)/3 = 2683 is prime.
Initial terms and associated primes:
a(1) = 0, 19;
a(2) = 1, 43;
a(3) = 2, 283;
a(4) = 3, 2683;
a(5) = 4, 26683;
a(6) = 5, 266683, etc.

Links

Crossrefs

Cf. A056654, A268448, A269303, A270339, A270613, A270831.

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[(8*10^# + 49)/3] &]
  • PARI
    is(n)=isprime((8*10^n + 49)/3) \\ Charles R Greathouse IV, Feb 16 2017

Extensions

a(38)-a(40) from Robert Price, May 23 2020

A270929 Numbers k such that (16*10^k - 31)/3 is prime.

Original entry on oeis.org

1, 2, 3, 4, 15, 20, 24, 32, 38, 40, 63, 93, 104, 194, 208, 514, 535, 600, 928, 1300, 1485, 1780, 2058, 3060, 3356, 3721, 6662, 11552, 15482, 23000, 27375, 34748, 57219, 61251, 85221, 99656, 103214, 103244, 276537
Offset: 1

Views

Author

Robert Price, Mar 26 2016

Keywords

Comments

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 3 followed by the digits 23 is prime (see Example section).
a(40) > 3*10^5. - Robert Price, Jul 13 2023

Examples

			3 is in this sequence because (16*10^3 - 31)/3 = 5323 is prime.
Initial terms and associated primes:
a(1) = 1, 43;
a(2) = 2, 523;
a(3) = 3, 5323;
a(4) = 4, 53323;
a(5) = 15, 5333333333333323;
a(6) = 20, 533333333333333333323, etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[(16*10^# - 31)/3] &]
  • PARI
    isok(n) = ispseudoprime((16*10^n - 31)/3); \\ Michel Marcus, Mar 26 2016

Extensions

a(37)-a(38) from Robert Price, Mar 03 2019
a(39) from Robert Price, Jul 13 2023

A271269 Numbers k such that 8*10^k - 49 is prime.

Original entry on oeis.org

1, 2, 3, 8, 24, 49, 57, 74, 104, 131, 144, 162, 182, 246, 302, 352, 557, 581, 589, 704, 939, 1181, 1937, 2157, 4463, 6013, 7266, 8504, 8691, 16129, 20108, 40677, 74234, 112018
Offset: 1

Views

Author

Robert Price, Apr 03 2016

Keywords

Comments

For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 9 followed by the digits 51 is prime (see Example section).
a(35) > 2*10^5.

Examples

			3 is in this sequence because 8*10^3 - 49 = 7951 is prime.
Initial terms and associated primes:
a(1) = 1, 31;
a(2) = 2, 751;
a(3) = 3, 7951;
a(4) = 8, 799999951;
a(6) = 24, 7999999999999999999999951, etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[8*10^# - 49] &]
  • PARI
    is(n)=isprime(8*10^n - 49) \\ Charles R Greathouse IV, Feb 16 2017

Extensions

a(34) from Robert Price, Aug 20 2019

A097683 Numbers k such that R_k + 2 is prime, where R_k = 11...1 is the repunit (A002275) of length k.

Original entry on oeis.org

0, 1, 2, 3, 5, 9, 11, 24, 84, 221, 1314, 2952, 20016, 51054
Offset: 1

Views

Author

Carl R. White and Julien Peter Benney (jpbenney(AT)ftml.net), Aug 19 2004

Keywords

Comments

Also numbers k such that (10^k + 17)/9 is prime.
The corresponding values R_k + 2 are primes of the form "(n-1) ones followed by a three"; zero is a degenerate case. Related to the base-10 repunit primes.
a(15) > 10^5. - Robert Price, Oct 12 2014
By Kamada link, a(15) > 4*10^5. - Jeppe Stig Nielsen, Jan 17 2023

Examples

			11113 = ((10^5)+17)/9 and 11113 is prime.

Links

Crossrefs

Cf. A002275, A004023, A056654, A097684, A097685.

Programs

  • Maple
    A097683:=n->`if`((10^n+17 mod 9) = 0 and isprime(floor((10^n+17)/9)),n,NULL): seq(A097683(n), n=0..10^3); # Wesley Ivan Hurt, Oct 12 2014
  • Mathematica
    Do[ If[ PrimeQ[(10^n - 1)/9 + 2], Print[n]], {n, 0, 5951}] (* Robert G. Wilson v, Oct 15 2004 *)

Formula

a(n) = A056654(n-1) + 1.

Extensions

a(11)-a(12) from Robert G. Wilson v, Oct 15 2004
Edited by N. J. A. Sloane, Apr 02 2009, at the suggestion of Farideh Firoozbakht
a(13) from Kamada link by Ray Chandler, Dec 23 2010
a(14) from Robert Price, Oct 12 2014

A093011 Primes of the form 10*R_k + 3, where R_k is the repunit (A002275) of length k.

Original entry on oeis.org

3, 13, 113, 11113, 111111113, 11111111113, 111111111111111111111113, 111111111111111111111111111111111111111111111111111111111111111111111111111111111113
Offset: 1

Views

Author

Rick L. Shepherd, Mar 14 2004

Keywords

Comments

Primes of the form 2 + (10^k - 1)/9, k > 0. - Vincenzo Librandi, Dec 13 2011

Links

Crossrefs

Cf. A056654 (corresponding k).

Programs

  • Magma
    [a: n in [1..100] | IsPrime(a) where a is ((10^n-1) div 9)+2 ]; // Vincenzo Librandi, Dec 13 2011
  • Mathematica
    Select[Table[(((10^n-1)/ 9)+2),{n,1,900}],PrimeQ] (* Vincenzo Librandi, Dec 13 2011 *)
Showing 1-10 of 507 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.