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 1-2 of 2 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

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
Showing 1-2 of 2 results.