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 1-7 of 7 results.

A068650 Primes in which a string of 1's is sandwiched between two 3's.

Original entry on oeis.org

313, 3111111111113, 311111111111113, 3111111111111111111111111111113, 311111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111113
Offset: 1

Views

Author

Amarnath Murthy, Feb 28 2002

Keywords

Comments

The next term (a(6)) has 127 digits. - Harvey P. Dale, Dec 18 2022

Crossrefs

Programs

  • Maple
    a := 3:b := 1:i := 1:for n from 0 to 500 do c := a+10*(10^n-1)/9*b+10^(n+1)*a; if(isprime(c)) then d[i] := c; i := i+1; end if; end do:q := seq(d[j],j=1..i-1);
  • Mathematica
    Select[Table[10*FromDigits[PadRight[{3},n,1]]+3,{n,2,110}],PrimeQ] (* Harvey P. Dale, Dec 18 2022 *)

Extensions

More terms from Sascha Kurz, Mar 19 2002
Edited by Ray Chandler, Nov 04 2014

A068646 Primes in which a string of 5's is sandwiched between two 1's.

Original entry on oeis.org

11, 151, 15551, 155555555555555555551, 155555555555555555555555555555551
Offset: 1

Views

Author

Amarnath Murthy, Feb 28 2002

Keywords

Comments

The next term is too big to include. - Sascha Kurz, Mar 19 2002

Examples

			11 is also a member in which a string of 0 5's is there between two one's.
		

Crossrefs

Programs

  • Maple
    a := 1:b := 5:i := 1:for n from 0 to 500 do c := a+10*(10^n-1)/9*b+10^(n+1)*a; if(isprime(c)) then d[i] := c; i := i+1; end if; end do:q := seq(d[j],j=1..i-1);
  • Mathematica
    Select[Table[FromDigits[Join[PadRight[{1},n,5],{1}]],{n,500}],PrimeQ] (* Harvey P. Dale, Aug 08 2012 *)

Extensions

More terms from Sascha Kurz, Mar 19 2002
Edited by Ray Chandler, Nov 04 2014

A068647 Primes in which a string of 6's is sandwiched between two 1's.

Original entry on oeis.org

11, 16661, 1666666666661, 16666666666666661, 1666666666666666661, 1666666666666666666666666666666666661, 16666666666666666666666666666666666666666666666666661
Offset: 1

Views

Author

Amarnath Murthy, Feb 28 2002

Keywords

Comments

The next term -- a(8) -- has 73 digits. - Harvey P. Dale, Jun 18 2021

Examples

			11 is also a member in which a string of 0 6's is there between two one's.
		

Crossrefs

Programs

  • Mathematica
    Select[Table[10*FromDigits[PadRight[{1},n,6]]+1,{n,60}],PrimeQ] (* Harvey P. Dale, Jun 18 2021 *)

Extensions

More terms from Sascha Kurz, Mar 19 2002
Edited by Ray Chandler, Nov 04 2014

A056265 Indices of primes in sequence defined by A(0) = 99, A(n) = 10*A(n-1) - 61 for n > 0.

Original entry on oeis.org

1, 5, 11, 109, 3607, 37783
Offset: 1

Views

Author

Robert G. Wilson v, Aug 18 2000

Keywords

Comments

Numbers n such that (830*10^n + 61)/9 is prime. - Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004
Numbers n such that digit 9 followed by n >= 0 occurrences of digit 2 followed by digit 9 is prime.
Numbers corresponding to terms <= 3607 are certified primes. For number corresponding to 37783 see P. De Geest, PDP Reference Table.

Examples

			9222229 is prime, hence 5 is a term.
		

References

  • Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

Crossrefs

Programs

  • Magma
    [n: n in [0..1000] | IsPrime((830*10^n + 61) div 9)]; // Vincenzo Librandi, Nov 02 2014
  • Mathematica
    Do[If[PrimeQ[(9*10^n + 2*(10^n - 1)/9)*10 + 9], Print[n]], {n, 1, 2500}]
    Select[Range[2000], PrimeQ[(830 10^# + 61) / 9] &] (* Vincenzo Librandi, Nov 02 2014 *)
  • PARI
    a=99;for(n=0,1000,if(isprime(a),print1(n,","));a=10*a-61) \\ Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004
    
  • PARI
    for(n=0,1000,if(isprime((830*10^n + 61)/9),print1(n,","))) \\ Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004
    

Formula

a(n) = A082718(n) - 2.

Extensions

3607 from Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004
37783 from Patrick De Geest, Jun 26 2005
Edited by N. J. A. Sloane, Jan 14 2008
Edited by Ray Chandler, Oct 20 2010
Comments section edited by Patrick De Geest, Nov 02 2014
Editied by Ray Chandler, Nov 05 2014

A068648 Primes in which a string of 8's is sandwiched between two 1's.

Original entry on oeis.org

11, 181, 188888881, 188888888888881, 18888888888888888888888888888888888888881, 188888888888888888888888888888888888888888888888888888888888888888888888888888888888888888881
Offset: 1

Views

Author

Amarnath Murthy, Feb 28 2002

Keywords

Comments

The next term -- a(7) -- has 129 digits. - Harvey P. Dale, Jul 08 2020

Examples

			11 is also a member in which a string of 0 8's is there between two one's.
		

Crossrefs

Programs

  • Maple
    a := 1:b := 8:i := 1:for n from 0 to 500 do c := a+10*(10^n-1)/9*b+10^(n+1)*a; if(isprime(c)) then d[i] := c; i := i+1; end if; end do:q := seq(d[j],j=1..i-1);
  • Mathematica
    Select[Table[10FromDigits[PadRight[{1},n,8]]+1,{n,100}],PrimeQ] (* Harvey P. Dale, Jul 08 2020 *)

Extensions

More terms from Sascha Kurz, Mar 19 2002
Edited by Ray Chandler, Nov 04 2014

A068649 Primes in which a string of 9's is sandwiched between two 1's.

Original entry on oeis.org

11, 191, 19991, 199999991, 19999999999999999999999999999999999999991, 199999999999999999999999999999999999999999999999999999999999999999999999999999999999991
Offset: 1

Views

Author

Amarnath Murthy, Feb 28 2002

Keywords

Comments

The next term has 199 9's sandwiched between the starting and ending 1.

Examples

			11 is also a member in which a string of 0 9's is there between two one's.
		

Crossrefs

Programs

  • Maple
    a := 1:b := 9:i := 1:for n from 0 to 500 do c := a+10*(10^n-1)/9*b+10^(n+1)*a; if(isprime(c)) then d[i] := c; i := i+1; end if; end do:q := seq(d[j],j=1..i-1);
  • Mathematica
    Select[Table[FromDigits[Join[{1}, Table[9, {i}], {1}]], {i, 0, 200}], PrimeQ]

Extensions

More terms from Sascha Kurz and Harvey P. Dale, Mar 19 2002
Edited by Ray Chandler, Nov 04 2014

A082718 Numbers k such that (83*10^(k-1) + 61)/9 is a depression prime.

Original entry on oeis.org

3, 7, 13, 111, 3609, 37785
Offset: 1

Views

Author

Patrick De Geest, Apr 13 2003

Keywords

Comments

Prime versus probable prime status and proofs are given in the author's table.

Examples

			k=13 -> (83*10^(13-1) + 61)/9 = 9222222222229.
		

References

  • C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.

Crossrefs

Formula

a(n) = A056265(n) + 2.

Extensions

37785 from Patrick De Geest, Jun 26 2005
Edited by Ray Chandler, Oct 20 2010
Edited by Ray Chandler, Nov 04 2014
Showing 1-7 of 7 results.