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 1-3 of 3 results.

A274676 Numbers k such that 7*10^k + 13 is prime.

Original entry on oeis.org

1, 3, 9, 12, 18, 19, 36, 37, 49, 67, 337, 893, 1924, 8044, 11610, 13560, 18777, 35376, 53601, 56022, 66488, 89801, 190210
Offset: 1

Views

Author

Vincenzo Librandi, Jul 03 2016

Keywords

Comments

a(15) > 10000. - Felix Fröhlich, Jul 03 2016

Examples

			3 is in this sequence because 7*10^3 + 13 = 7013 is prime.
4 is not in the sequence because 7*10^4 + 13 = 70013 = 53 * 1321.
Initial terms and associated primes:
a(1) =  1: 83;
a(2) =  3: 7013;
a(3) =  9: 7000000013;
a(4) = 12: 7000000000013, etc.

Links

Crossrefs

Cf. numbers k such that 7*10^k + m is prime: A056804 (m=1), A097970 (m=3), A097954 (m=9), this sequence (m=13), A274677 (m=19), A274678 (m=27), A111021 (m=31), A274679 (m=33), A274700 (m=37), A274692 (m=43), A270974 (m=57).

Programs

  • Magma
    [n: n in [1..800] | IsPrime(7*10^n+13)];
  • Maple
    select(t -> isprime(7*10^t+13), [$1..2000]); # Robert Israel, Jul 03 2016
  • Mathematica
    Select[Range[0, 3000], PrimeQ[7 * 10^# + 13] &]
  • PARI
    is(n) = ispseudoprime(7*10^n+13) \\ Felix Fröhlich, Jul 03 2016
  • PARI
    lista(nn) = for(n=1, nn, if(ispseudoprime(7*10^n+13), print1(n, ", "))); \\ Altug Alkan, Jul 03 2016

Extensions

a(15) from Michael S. Branicky, Jan 22 2023
a(16)-a(17) from Michael S. Branicky, Apr 10 2023
a(18)-a(23) from Kamada data by Tyler Busby, Apr 15 2024

A271107 Numbers k such that 33*10^k + 1 is prime.

Original entry on oeis.org

1, 2, 5, 6, 7, 8, 29, 47, 145, 205, 227, 505, 553, 600, 787, 809, 1305, 1447, 1593, 2285, 4763, 5679, 9133, 12516, 14869, 16536, 33402, 36085, 51933, 56443, 69133
Offset: 1

Views

Author

Robert Price, Mar 30 2016

Keywords

Comments

Numbers k such that the digits 33 followed by k-1 occurrences of the digit 0 followed by the digit 1 is prime (see Example section).
a(32) > 10^5.

Examples

			5 is in this sequence because 33*10^5+1 = 3300001 is prime.
Initial terms and associated primes:
a(1) = 1, 331;
a(2) = 2, 3301;
a(3) = 5, 3300001;
a(4) = 6, 33000001;
a(5) = 7, 330000001;
a(6) = 8, 3300000001, etc.

Links

Crossrefs

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A270974.

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[33*10^#+1] &]
  • PARI
    lista(nn) = for(n=1, nn, if(ispseudoprime(33*10^n+1), print1(n, ", "))); \\ Altug Alkan, Mar 31 2016

A271146 Numbers k such that (16*10^k - 19)/3 is prime.

Original entry on oeis.org

1, 4, 5, 6, 10, 13, 20, 22, 24, 35, 41, 42, 46, 155, 222, 336, 432, 538, 577, 637, 679, 750, 758, 785, 2262, 5436, 6806, 7962, 9757, 16016, 24588, 47918, 59062, 74092, 81896, 85495, 102299, 185978, 190420
Offset: 1

Views

Author

Robert Price, Mar 31 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 27 is prime (see Example section).
a(40) > 2*10^5.

Examples

			4 is in this sequence because (16*10^4 - 19)/3 = 53327 is prime.
Initial terms and associated primes:
a(1) = 1, 47;
a(2) = 4, 53327;
a(3) = 5, 533327;
a(4) = 6, 5333327;
a(5) = 10, 53333333327;
a(6) = 13, 53333333333327, etc.

Links

Crossrefs

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A270974.

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[(16*10^# - 19)/3] &]
  • PARI
    lista(nn) = {for(n=1, nn, if(ispseudoprime((16*10^n - 19)/3), print1(n, ", ")));} \\ Altug Alkan, Mar 31 2016

Extensions

a(37)-a(39) from Robert Price, Feb 23 2019
Showing 1-3 of 3 results.

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