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.

A082697 Numbers k such that (4*10^(k-1) - 7)/3 is a plateau prime.

Original entry on oeis.org

3, 5, 7, 95, 161, 361, 1471, 2899, 3095, 3113, 15699, 17957, 42263, 111033
Offset: 1

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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=7 -> (4*10^(7-1) - 7)/3 = 1333331.
		

References

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

Crossrefs

Formula

a(n) = A056244(n+1) + 2.

Extensions

a(13)=42263 from Patrick De Geest, Oct 03 2004
a(14)=111033 from Ray Chandler, Apr 14 2011
Edited by Ray Chandler, Nov 04 2014

A068651 Primes in which a string of 2's is sandwiched between two 9's.

Original entry on oeis.org

929, 9222229, 9222222222229
Offset: 1

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Author

Amarnath Murthy, Feb 28 2002

Keywords

Comments

The next term consists of 109 2's sandwiched between two 9's. - Sascha Kurz, Mar 27 2002

Crossrefs

Formula

a(n) = (830*10^A056265(n) + 61)/9 = (83*10^(A082718(n)-1) + 61)/9. [corrected by Amiram Eldar, Jul 27 2025]

Extensions

Edited by Ray Chandler, Oct 20 2010
Edited by Ray Chandler, Nov 05 2014

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

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

A056244 Indices of primes in sequence defined by A(0) = 11, A(n) = 10*A(n-1) + 21 for n > 0.

Original entry on oeis.org

0, 1, 3, 5, 93, 159, 359, 1469, 2897, 3093, 3111, 15697, 17955, 42261, 111031
Offset: 1

Views

Author

Robert G. Wilson v, Aug 18 2000

Keywords

Comments

Numbers n such that (120*10^n - 21)/9 is prime.
Numbers n such that digit 1 followed by n >= 0 occurrences of digit 3 followed by digit 1 is prime.
Numbers corresponding to terms <= 3111 are certified primes. For larger numbers see P. De Geest, PDP Reference Table.

Examples

			131 is prime, hence 1 is a term.
		

References

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

Crossrefs

Programs

  • Mathematica
    Do[If[PrimeQ[(1*10^n + 3*(10^n - 1)/9)*10 + 1], Print[n]], {n, 1, 2500}]
    Select[Range[0, 2000], PrimeQ[(120 10^# - 21) / 9] &] (* Vincenzo Librandi, Nov 03 2014 *)
  • PARI
    a=11;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+21)
    
  • PARI
    for(n=0,1500,if(isprime((120*10^n-21)/9),print1(n,",")))

Formula

a(n) = A082697(n-1) - 2 for n > 1.

Extensions

More terms and additional comments from Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004
Edited by N. J. A. Sloane, Jun 15 2007
Updates from De Geest site by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
a(15)=111031 from Ray Chandler, Apr 14 2011
Updated comments section and a link, by Patrick De Geest, Nov 02 2014
Edited by Ray Chandler, Nov 04 2014
Showing 1-8 of 8 results.