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 1-4 of 4 results.

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

Views

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

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

A056246 Indices of primes in sequence defined by A(0) = 11, A(n) = 10*A(n-1) + 41 for n > 0.

Original entry on oeis.org

0, 1, 3, 19, 31, 399, 561, 7015, 37683
Offset: 1

Views

Author

Robert G. Wilson v, Aug 18 2000

Keywords

Comments

Numbers n such that (140*10^n - 41)/9 is a prime.
Numbers n such that digit 1 followed by n >= 0 occurrences of digit 5 followed by digit 1 is a prime.
Numbers corresponding to terms <= 561 are certified primes.

Examples

			151 is a 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
    Select[Range[0, 2000], PrimeQ[(140 10^# - 41) / 9] &] (* Vincenzo Librandi, Nov 03 2014 *)
  • PARI
    a=11;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+41)
    
  • PARI
    for(n=0,1500,if(isprime((140*10^n-41)/9),print1(n,",")))

Formula

a(n) = A082699(n-1) - 2 for n > 1.

Extensions

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
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
Added and updated a link, by Patrick De Geest, Nov 02 2014
Edited by Ray Chandler, Nov 04 2014

A082699 Numbers k such that (14*10^(k-1) - 41)/9 is a plateau prime.

Original entry on oeis.org

3, 5, 21, 33, 401, 563, 7017, 37685
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=21 -> (14*10^(21-1) - 41)/9 = 155555555555555555551.
		

References

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

Crossrefs

Formula

a(n) = A056246(n+1) + 2.

Extensions

37685 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
Edited by Ray Chandler, Nov 04 2014
Showing 1-4 of 4 results.