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 1-3 of 3 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

A082703 Numbers k such that (18*10^(k-1) - 81)/9 is a plateau prime.

Original entry on oeis.org

3, 5, 9, 41, 87, 201, 731, 1461, 23673, 28631
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=9 -> (18*10^(9-1) - 81)/9 = 199999991.
		

References

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

Crossrefs

Formula

a(n) = A056250(n+1) + 2.

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
Edited by Ray Chandler, Nov 04 2014

A056250 Indices of primes in sequence defined by A(0) = 11, A(n) = 10*A(n-1) + 81 for n > 0.

Original entry on oeis.org

0, 1, 3, 7, 39, 85, 199, 729, 1459, 23671, 28629
Offset: 1

Views

Author

Robert G. Wilson v, Aug 18 2000

Keywords

Comments

Numbers n such that (180*10^n - 81)/9 is prime.
Numbers n such that digit 1 followed by n >= 0 occurrences of digit 9 followed by digit 1 is prime.
Numbers corresponding to terms <= 1459 are certified primes. For larger numbers see P. De Geest, PDP Reference Table.

Examples

			191 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
    Select[Range[0, 2000], PrimeQ[(180 10^# - 81) / 9] &] (* Vincenzo Librandi, Nov 03 2014 *)
  • PARI
    a=11;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+81)
    
  • PARI
    for(n=0,1500,if(isprime((180*10^n-81)/9),print1(n,",")))

Formula

a(n) = A082703(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
Updated comments section and a link, by Patrick De Geest, Nov 02 2014
Edited by Ray Chandler, Nov 04 2014
Showing 1-3 of 3 results.