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 497 results. Next

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

A270974 Numbers k such that 7*10^k + 57 is prime.

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 12, 14, 19, 21, 27, 33, 60, 61, 91, 102, 535, 549, 614, 695, 709, 1014, 2448, 2519, 3464, 3511, 6348, 6841, 11009, 11177, 20754, 26610, 30651, 39246, 122294
Offset: 1

Views

Author

Robert Price, Mar 27 2016

Keywords

Comments

For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 0 followed by the digits 57 is prime (see Example section).
a(35) > 2*10^5.

Examples

			3 is in this sequence because 7*10^3+57 = 7057 is prime.
Initial terms and associated primes:
a(1) = 1, 127;
a(2) = 2, 757;
a(3) = 3, 7057;
a(4) = 5, 700057;
a(5) = 6, 7000057;
a(6) = 7, 70000057, etc.

Links

Crossrefs

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

Programs

  • Magma
    [n: n in [1..500] | IsPrime(7*10^n + 57)]; // Vincenzo Librandi, Jul 03 2016
  • Mathematica
    Select[Range[0, 100000], PrimeQ[7*10^# + 57] &]
  • PARI
    lista(nn) = {for(n=1, nn, if(ispseudoprime(7*10^n + 57), print1(n, ", ")));} \\ Altug Alkan, Mar 27 2016

Extensions

a(35) from Robert Price, Jun 13 2019

A254441 Numbers k such that (41*10^k + 49)/9 is prime.

Original entry on oeis.org

2, 3, 6, 20, 26, 38, 51, 119, 155, 218, 446, 486, 1211, 1319, 1338, 1365, 1575, 5106, 7019, 9503, 9695, 14304, 15417, 17765, 24222, 25500, 26306, 35238, 93207
Offset: 1

Views

Author

Robert Price, Apr 17 2016

Keywords

Comments

For terms k > 1, numbers that begin with the digit 4 followed by k-2 occurrences of the digit 5 followed by the digits 61 are prime (see Example section).
a(30) > 2*10^5.

Examples

			3 is in this sequence because (41*10^3 + 49)/9 = 4561 is prime.
Initial terms and associated primes:
a(1) = 2, 461;
a(2) = 3, 4561;
a(3) = 6, 4555561;
a(4) = 20, 455555555555555555561;
a(5) = 26, 455555555555555555555555561, etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[(41*10^# + 49)/9] &]
  • PARI
    is(n)=ispseudoprime((41*10^n + 49)/9) \\ Charles R Greathouse IV, Jun 13 2017

A271109 Numbers k such that (5 * 10^k - 119)/3 is prime.

Original entry on oeis.org

2, 3, 5, 6, 8, 11, 26, 33, 35, 41, 69, 73, 204, 230, 295, 381, 392, 537, 776, 1187, 2187, 2426, 4182, 4589, 5841, 6107, 11513, 13431, 28901, 56256, 65203, 66613, 82085, 91707, 126871, 140281
Offset: 1

Views

Author

Robert Price, Apr 05 2016

Keywords

Comments

For k > 1, numbers k such that the digit 1 followed by k - 2 occurrences of the digit 6 followed by the digits 27 is prime (see Example section).
a(37) > 2*10^5.

Examples

			3 is in this sequence because (5*10^3 - 119)/3 = 1627 is prime.
Initial terms and associated primes:
a(1) = 2, 127;
a(2) = 3, 1627;
a(3) = 5, 166627;
a(4) = 6, 1666627;
a(5) = 8, 166666627, etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[10^5], PrimeQ[(5 * 10^# - 119)/3] &]
  • PARI
    is(n)=ispseudoprime((5*10^n-119)/3) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(35)-a(36) from Robert Price, Mar 29 2018

A273002 Numbers k such that 16*10^k + 1 is prime.

Original entry on oeis.org

0, 2, 3, 4, 18, 21, 36, 58, 68, 78, 84, 94, 150, 178, 190, 591, 686, 812, 840, 2308, 2530, 2884, 4311, 6134, 7695, 8004, 8109, 9777, 15570, 17505
Offset: 1

Views

Author

Robert Price, May 12 2016

Keywords

Comments

For k > 1, numbers k such that the digits 16 followed by k-1 occurrences of the digit 0 followed by the digit 1 is prime (see Example section).
a(31) > 10^5.

Examples

			4 is in this sequence because 16*10^4+1 = 160001 is prime.
Initial terms and associated primes:
a(1) = 0, 17;
a(2) = 2, 1601;
a(3) = 3, 16001;
a(4) = 4, 160001;
a(5) = 18, 16000000000000000001. etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[16*10^#+1] &]
  • PARI
    is(n)=ispseudoprime(16*10^n+1) \\ Charles R Greathouse IV, Jun 13 2017

A274692 Numbers k such that 7*10^k + 43 is prime.

Original entry on oeis.org

1, 2, 3, 7, 26, 27, 36, 44, 50, 57, 59, 73, 124, 152, 154, 250, 271, 301, 376, 451, 1177, 2299, 3740, 13159, 14780, 17435, 30098, 32521
Offset: 1

Views

Author

Robert Price, Jul 02 2016

Keywords

Comments

For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 0 followed by the digits 43 is prime (see Example section).
a(29) > 10^5.

Examples

			3 is in this sequence because 7*10^3 + 43 = 7043 is prime.
Initial terms and associated primes:
a(1) = 1, 113;
a(2) = 2, 743;
a(3) = 3, 7043;
a(4) = 7, 70000043;
a(5) = 26, 700000000000000000000000043, etc.

Links

Crossrefs

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

Programs

  • Magma
    [n: n in [1..400] | IsPrime(7*10^n + 43)]; // Vincenzo Librandi, Jul 03 2016
  • Mathematica
    Select[Range[0, 100000], PrimeQ[7*10^# + 43] &]
  • PARI
    lista(nn) = for(n=1, nn, if(ispseudoprime(7*10^n + 43), print1(n, ", "))); \\ Altug Alkan, Jul 02 2016

A278397 Numbers k such that 10^k - 20001 is prime.

Original entry on oeis.org

5, 11, 16, 21, 37, 83, 94, 299, 318, 467, 622, 707, 1931, 2175, 2189, 2238, 2526, 5202, 10541, 15822, 17407, 19919, 19998, 25407, 96377, 118009
Offset: 1

Views

Author

Robert Price, Nov 20 2016

Keywords

Comments

For k > 4, numbers k such that k-5 occurrences of the digit 9 followed by the digits 79999 is prime (see Example section).
a(27) > 2*10^5.

Examples

			5 is in this sequence because 10^5 - 20001 = 79999 is prime.
Initial terms and associated primes:
a(1) = 5, 79999;
a(2) = 11, 99999979999;
a(3) = 16, 9999999999979999;
a(4) = 21, 999999999999999979999;
a(5) = 37, 9999999999999999999999999999999979999; etc.

Links

Crossrefs

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

Programs

  • Magma
    [n: n in [5..400] | IsPrime(10^n - 20001)]; // Vincenzo Librandi, Nov 21 2016
  • Mathematica
    Select[Range[0, 100000], PrimeQ[10^# - 20001] &]
  • PARI
    is(n)=ispseudoprime(10^n-20001) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(26) from Robert Price, Jan 26 2018

A281171 Numbers k such that (5*10^k + 37)/3 is prime.

Original entry on oeis.org

1, 2, 5, 9, 13, 20, 21, 32, 33, 56, 73, 81, 149, 313, 455, 753, 1013, 1166, 1304, 1679, 15758, 15896, 21801, 41353, 45421, 131090, 151007
Offset: 1

Views

Author

Robert Price, Jan 16 2017

Keywords

Comments

For k > 1, numbers k such that the digit 1 followed by k-2 occurrences of the digit 6 followed by the digits 79 is prime (see Example section).
a(28) > 2*10^5.

Examples

			2 is in this sequence because (5*10^2 + 37) / 3 = 179 is prime.
Initial terms and associated primes:
a(1) = 1, 29;
a(2) = 2, 179;
a(3) = 5, 166679;
a(4) = 9, 1666666679;
a(5) = 13, 16666666666679; etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[(5*10^# + 37) / 3] &]

Extensions

a(26)-a(27) from Robert Price, Mar 02 2018

A281732 Numbers k such that (8*10^k + 67)/3 is prime.

Original entry on oeis.org

3, 5, 9, 20, 26, 77, 101, 120, 308, 543, 869, 876, 1193, 1199, 1355, 1923, 3689, 3788, 4182, 6539, 19068, 26922, 38957, 58872, 61230, 72759
Offset: 1

Views

Author

Robert Price, Jan 28 2017

Keywords

Comments

For k > 1, numbers k such that the digit 2 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

			5 is in this sequence because (8*10^5 + 67)/3 = 2266689 7751 is prime.
Initial terms and associated primes:
a(1) = 3, 2689;
a(2) = 5, 266689;
a(3) = 9, 2666666689;
a(4) = 20, 266666666666666666689; etc.

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0, 100000], PrimeQ[(8*10^# + 67)/3] &]
Showing 1-10 of 497 results. Next

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