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 1-8 of 8 results.

A120819 Indices of primes in A057137.

Original entry on oeis.org

171, 277, 367, 561, 567, 18881
Offset: 1

Views

Author

Robert G. Wilson v, Jul 05 2006

Keywords

Comments

Digits are in ascending order beginning with 1 and after 9 comes 0.
Indices of primes in A057137.
All terms must end in 1 or 7: A057137(n) is even when n is even, and divisible by 3 iff n == 0, 2, 3, 5, 6, 8 or 9 (mod 10). - M. F. Hasler, Apr 14 2024
a(7) >= 100000. - Michael S. Branicky, Apr 07 2025

Examples

			a(1) = 12345678901234567890...01234567890...012345678901 = A057137(171) is the first prime term in A057137.

References

  • Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 61, 298.

Crossrefs

Cf. A006055, A057137, A120828, A120820, A120821, A120822, A120823, A120824, A120825, A120826, A120827.

Programs

  • Mathematica
    fQ[n_] := PrimeQ@ FromDigits@ Mod[Range@n, 10]; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]; Print@n], {n, 10000}]; lst
IntegerLength[Select[Table[FromDigits[PadRight[{},n,{1,2,3,4,5,6,7,8,9,0}]],{n,1,1001,2}],PrimeQ]] (* Harvey P. Dale, Feb 07 2024 *)
  • PARI
    N=0;for(n=1,600,if(ispseudoprime(N=10*N+n%10),print1(n", "))) \\ Charles R Greathouse IV, May 10 2014  (Comment: Surprisingly, this is faster than calling ispseudoprime() only when n ends in 1 or 7, even when much larger N's are considered, e.g., up to 3000. - M. F. Hasler, Apr 14 2024)
  • Python
    from sympy import isprime
L = ['8901', '234567']; s = '1234567'; c = len(s); m = 0
while c < 18881:
    s += L[m%2]; c = len(s); m += 1
    if isprime(int(s)): print(c, end = ', ')  # Ya-Ping Lu, Jan 24 2025

Extensions

a(6) from Arjen Lenstra, Feb 20 2012

A120821 a(n) consecutive digits ascending beginning with the digit 3 give a prime.

Original entry on oeis.org

1, 179, 529, 62625
Offset: 1

Views

Author

Robert G. Wilson v, Jul 05 2006

Keywords

Comments

Digits are in ascending order beginning with 3 and after 9 comes 0.
The sequence "a(n) consecutive digits descending beginning with the digit 3 give a prime." has only one term, 1 which represents the prime 3.
a(5) > 10^5. - Michael S. Branicky, Apr 08 2025

Crossrefs

Cf. A006055, A120819, A120820, A120822, A120823, A120824, A120825, A120826, A120827.

Programs

  • Mathematica
    fQ[n_] := PrimeQ@ FromDigits@ Mod[2+Range@n, 10]; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]; Print@n], {n, 10000}]; lst

Extensions

a(4) from Michael S. Branicky, Apr 03 2025

A120822 a(n) consecutive digits ascending beginning with the digit 4 give a prime.

Original entry on oeis.org

4, 8, 194
Offset: 1

Views

Author

Robert G. Wilson v, Jul 05 2006

Keywords

Comments

Digits are in ascending order beginning with 4; after 9 comes 0.
a(4) > 10^5. - Michael S. Branicky, Apr 08 2025

Examples

			8 is a term since 45678901 is a prime.

Crossrefs

Cf. A006055, A120829, A120819, A120820, A120821, A120823, A120824, A120825, A120826, A120827.

Programs

  • Mathematica
    fQ[n_] := PrimeQ@ FromDigits@ Mod[3+Range@n, 10]; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]; Print@n], {n, 10000}]; lst

A120820 a(n) consecutive digits ascending beginning with the digit 2 give a prime.

Original entry on oeis.org

1, 2, 8, 82, 118, 158, 2122, 2242, 2388
Offset: 1

Views

Author

Robert G. Wilson v, Jul 05 2006

Keywords

Comments

Digits are in ascending order beginning with 2 and after 9 comes 0.
The sequence "a(n) consecutive digits descending beginning with the digit 2 give a prime" has only one term, 1 which represents the prime 2.
a(10) > 10^5. - Michael S. Branicky, Apr 10 2025

Examples

			8 is a term since 23456789 is a prime.

Crossrefs

Cf. A006055, A120819, A120821, A120822, A120823, A120824, A120825, A120826, A120827.

Programs

  • Mathematica
    fQ[n_] := PrimeQ@ FromDigits@ Mod[1+Range@n, 10]; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]; Print@n], {n, 10000}]; lst

A120823 a(n) consecutive digits ascending beginning with the digit 5 give a prime..

Original entry on oeis.org

1, 29, 269, 689
Offset: 1

Views

Author

Robert G. Wilson v, Jul 05 2006

Keywords

Comments

Digits are in ascending order beginning with 5 and after 9 comes 0.
The sequence "a(n) consecutive digits descending beginning with the digit 5 give a prime." has only one term, 1 which represents the prime 5.
a(5) > 10^5. - Michael S. Branicky, Apr 08 2025

Examples

			29 is a term since the 29-digit number 56789012345678901234567890123 is a prime.

Crossrefs

Cf. A006055, A120819, A120820, A120821, A120822, A120824, A120825, A120826, A120827.

Programs

  • Mathematica
    fQ[n_] := PrimeQ@ FromDigits@ Mod[4+Range@n, 10]; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]; Print@n], {n, 9000}]; lst

A120824 a(n) consecutive digits ascending beginning with the digit 6 give a prime.

Original entry on oeis.org

2, 6, 36, 122, 336, 82812
Offset: 1

Views

Author

Robert G. Wilson v, Jul 05 2006

Keywords

Comments

Digits are in ascending order beginning with 6 and after 9 comes 0.
The sequence "a(n) consecutive digits descending beginning with the digit 6 give a prime" has no terms.
a(7) >= 100000. - Michael S. Branicky, Apr 07 2025

Examples

			6 is a term since 678901 is a prime.

Crossrefs

Cf. A006055, A120819, A120820, A120821, A120822, A120823, A120825, A120826, A120827.

Programs

  • Mathematica
    fQ[n_] := PrimeQ@ FromDigits@ Mod[5+Range@n, 10]; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]; Print@n], {n, 5000}]; lst

Extensions

a(6) from Michael S. Branicky, Apr 05 2025

A120825 a(n) consecutive digits ascending beginning with the digit 7 give a prime.

Original entry on oeis.org

1, 5, 15, 51, 8411
Offset: 1

Views

Author

Robert G. Wilson v, Jul 05 2006

Keywords

Comments

Digits are in ascending order beginning with 7 and after 9 comes 0.
The sequence "a(n) consecutive digits descending beginning with the digit 7 give a prime" has only two terms below 6001, namely 1 and 5, which represent the primes 7 and 76543, respectively.
a(6) >= 100000. - Michael S. Branicky, Apr 07 2025

Examples

			1 is here because 7 is prime.
5 is here because 78901 is prime.
15 is here because 789012345678901 is a prime.
51 is here because 789012345678901234567890123456789012345678901234567 is prime.

Crossrefs

Cf. A006055, A120819, A120820, A120821, A120822, A120823, A120824, A120826, A120827.

Programs

  • Mathematica
    fQ[n_] := PrimeQ@ FromDigits@ Mod[6+Range@n, 10]; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]; Print@n], {n, 5000}]; lst

Extensions

a(5) from Bert Dobbelaere, Apr 01 2025

A120827 a(n) consecutive digits ascending beginning with the digit 9 give a prime.

Original entry on oeis.org

13, 29, 43
Offset: 1

Views

Author

Robert G. Wilson v, Jul 05 2006

Keywords

Comments

Digits are in ascending order beginning with 9 and after 9 comes 0.
The sequence "a(n) consecutive digits descending beginning with the digit 9 give a prime" has no terms.
There is no further term up to 26000. - Farideh Firoozbakht, Sep 11 2006
There is no further term up to 150000. - Michael S. Branicky, Apr 22 2025

Examples

			13 is a term since 9012345678901 is a prime.

Crossrefs

Cf. A006055, A120819, A120820, A120821, A120822, A120823, A120824, A120825, A120826.

Programs

  • Mathematica
    fQ[n_] := PrimeQ@ FromDigits@ Mod[8+Range@n, 10]; lst = {}; Do[ If[fQ@n, AppendTo[lst, n]; Print@n], {n, 5000}]; lst
Flatten[Position[Table[FromDigits[PadRight[{},n,{9,0,1,2,3,4,5,6,7,8}]],{n,100}],?PrimeQ]] (* _Harvey P. Dale, Sep 06 2015 *)
Showing 1-8 of 8 results.

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