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

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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

A056251 Indices of primes in sequence defined by A(0) = 33, A(n) = 10*A(n-1) - 17 for n > 0.

Original entry on oeis.org

1, 11, 13, 29, 103, 125, 341, 599, 9823
Offset: 1

Views

Author

Robert G. Wilson v, Aug 18 2000

Keywords

Comments

Numbers n such that (280*10^n + 17)/9 is prime.
Numbers n such that digit 3 followed by n >= 0 occurrences of digit 1 followed by digit 3 is prime.
Numbers corresponding to terms <= 599 are certified primes.
All terms are odd since 11 is the only palindromic prime with an even number of digits. - Chai Wah Wu, Nov 05 2019
a(10) > 2*10^5. - Tyler Busby, Feb 01 2023

Examples

			313 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

Formula

a(n) = A082704(n) - 2.

Extensions

Additional comments from Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 20 2004
Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 15 2007
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
Added and updated the links section, by Patrick De Geest, Nov 02 2014
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

A082704 Numbers k such that (28*10^(k-1) + 17)/9 is a depression prime.

Original entry on oeis.org

3, 13, 15, 31, 105, 127, 343, 601, 9825
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.
a(10) > 2^16. - Lucas A. Brown, Apr 18 2021
a(10) > 2*10^5. - Tyler Busby, Feb 01 2023

Examples

			k=15 -> (28*10^(15-1) + 17)/9 = 311111111111113.
		

References

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

Crossrefs

Formula

a(n) = A056251(n) + 2.

Extensions

Edited by Ray Chandler, Nov 04 2014
Showing 1-4 of 4 results.