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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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

A262937 Numbers k such that (28*10^k - 13) / 3 is prime.

Original entry on oeis.org

0, 1, 2, 4, 5, 8, 10, 14, 17, 20, 33, 64, 80, 152, 158, 166, 194, 196, 198, 901, 971, 1289, 1595, 2921, 14390, 28781, 35840
Offset: 1

Views

Author

Robert Price, Sep 23 2016

Keywords

Comments

For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 3 followed by the digits 29 is prime (see Example section).
a(28) > 3*10^5.

Examples

			2 is in this sequence because (28*10^2 - 13) / 3 = 929 is prime.
Initial terms and associated primes:
a(1) = 0, 5;
a(2) = 1, 89;
a(3) = 2, 929;
a(4) = 4, 93329;
a(5) = 5, 933329, etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[(28*10^# - 13) / 3] &]
  • PARI
    is(n)=ispseudoprime((28*10^n - 13)/3) \\ Charles R Greathouse IV, Jun 13 2017

A265938 Numbers k such that 6*10^k + 91 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 7, 10, 11, 14, 23, 31, 37, 42, 105, 106, 114, 137, 182, 212, 233, 313, 621, 629, 1067, 1570, 4612, 6288, 20030, 21843, 24800, 43694, 179970
Offset: 1

Views

Author

Robert Price, Apr 06 2016

Keywords

Comments

For k > 1, numbers k such that the digit 6 followed by k-2 occurrences of the digit 0 followed by the digits 91 is prime (see Example section).
a(34) > 3*10^5.

Examples

			3 is in this sequence because 6*10^3+91 = 6091 is prime.
Initial terms and associated primes:
a(1) = 0, 97;
a(2) = 1, 151;
a(3) = 2, 691;
a(4) = 3, 6091;
a(5) = 4, 60091, etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[6*10^# + 91] &]
  • PARI
    is(n)=ispseudoprime(6*10^n + 91) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(33) from Robert Price, May 21 2019

A266582 Numbers k such that (265*10^k - 7)/3 is prime.

Original entry on oeis.org

1, 2, 4, 9, 13, 14, 16, 46, 99, 112, 116, 127, 146, 208, 512, 848, 1132, 2167, 2482, 2666, 3625, 14410, 16567, 21529, 26272, 69554, 69602
Offset: 1

Views

Author

Robert Price, Jul 10 2016

Keywords

Comments

For k > 0, numbers k such that the digits 88 followed by k-1 occurrences of the digit 3 followed by the digit 1 is prime (see Example section).
a(28) > 10^5.

Examples

			4 is in this sequence because (265*10^4 - 7)/3 = 883331 is prime.
Initial terms and associated primes:
a(1) = 1, 881;
a(2) = 2, 8831;
a(3) = 4, 883331l
a(4) = 9, 88333333331;
a(5) = 13, 883333333333331, etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[(265*10^# - 7)/3] &]
  • PARI
    is(n)=ispseudoprime((265*10^n-7)/3) \\ Charles R Greathouse IV, Jun 13 2017

A267865 Numbers k such that 49*10^k + 1 is prime.

Original entry on oeis.org

1, 4, 5, 7, 9, 10, 18, 19, 34, 52, 71, 180, 238, 331, 370, 576, 925, 994, 1075, 1841, 2460, 2857, 6007, 6193, 10836, 18732, 58708, 72861
Offset: 1

Views

Author

Robert Price, Apr 07 2016

Keywords

Comments

Numbers k such that the digits 49 followed by k-1 occurrences of the digit 0 followed by the digit 1 is prime (see Example section).
a(29) > 10^5.

Examples

			4 is in this sequence because 49*10^4 + 1 = 490001 is prime.
Initial terms and associated primes:
a(1) = 1, 491;
a(2) = 4, 490001;
a(3) = 5, 4900001;
a(4) = 7, 490000001;
a(5) = 9, 49000000001, etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[49*10^#+1] &]
  • PARI
    is(n)=ispseudoprime(49*10^n+1) \\ Charles R Greathouse IV, Jun 13 2017

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

A271147 Numbers k such that (28*10^k + 113)/3 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 6, 9, 12, 16, 22, 23, 42, 52, 57, 63, 117, 119, 208, 266, 324, 481, 779, 1244, 1289, 2998, 5522, 5599, 5771, 6820, 12367, 14737, 22612, 30623, 31596, 58956, 59133, 138240, 163709, 250655, 259897
Offset: 1

Views

Author

Robert Price, Mar 31 2016

Keywords

Comments

For k > 1, numbers k such that the digit 9 followed by k-2 occurrences of the digit 3 followed by the digits 71 is prime (see Example section).
a(41) > 3*10^5.

Examples

			3 is in this sequence because (28*10^3+113)/3 = 9371 is prime.
Initial terms and associated primes:
a(1) = 0, 47;
a(2) = 1, 131;
a(3) = 2, 971;
a(4) = 3, 9371;
a(5) = 4, 93371;
a(6) = 6, 9333371, etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[(28*10^# + 113)/3] &]
  • PARI
    is(n)=ispseudoprime((28*10^n + 113)/3) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(37)-a(38) from Robert Price, Mar 13 2020
a(39)-a(40) from Robert Price, Jun 17 2023
Previous Showing 21-30 of 497 results. Next

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

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