A056265 -id:A056265 - cp's OEIS frontend

A057178 Numbers k such that (12^k + 1)/13 is a prime.

Original entry on oeis.org

5, 11, 109, 193, 1483, 11353, 21419, 21911, 24071, 106859, 139739, 495953

Offset: 1

N. J. A. Sloane, Sep 15 2000

nonn

(12^1483 + 1)/13, a 1600-digit number, has now been certified prime with Primo. - Rick L. Shepherd, May 01 2002

Paul Bourdelais, A Generalized Repunit Conjecture
J. Brillhart et al., Factorizations of b^n +- 1, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
H. Lifchitz, Mersenne and Fermat primes field
Eric Weisstein's World of Mathematics, Repunit

Different from A056265.

lst={};Do[p=(12^n+1)/13;If[PrimeQ[p], AppendTo[lst, n]], {n, 7!}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 29 2008 *)

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008
a(10) corresponds to a probable prime, discovered by Paul Bourdelais, Feb 08 2010
a(11) corresponds to a probable prime, discovered by Paul Bourdelais, Sep 21 2011
a(12) corresponds to a probable prime, discovered by Paul Bourdelais, Nov 13 2018

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

Amarnath Murthy, Feb 28 2002

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

Amiram Eldar, Table of n, a(n) for n = 1..4
Patrick De Geest, PDP Reference Table - 929.
Makoto Kamada, Prime numbers of the form 922...229.
Index entries for primes involving repunits.

Cf. A068645, A068646, A068647, A068648, A068649, A068650, A056265, A082718.

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

Edited by Ray Chandler, Oct 20 2010

Edited by Ray Chandler, Nov 05 2014

A082718 Numbers k such that (83*10^(k-1) + 61)/9 is a depression prime.

Original entry on oeis.org

3, 7, 13, 111, 3609, 37785

Offset: 1

Patrick De Geest, Apr 13 2003

Prime versus probable prime status and proofs are given in the author's table.

			k=13 -> (83*10^(13-1) + 61)/9 = 9222222222229.

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

Patrick De Geest, PDP Reference Table - 929.
Makoto Kamada, Prime numbers of the form 922...229.
Index entries for primes involving repunits.

Cf. A082697-A082720, A056265, A068651.

a(n) = A056265(n) + 2.

37785 from Patrick De Geest, Jun 26 2005
Edited by Ray Chandler, Oct 20 2010
Edited by Ray Chandler, Nov 04 2014

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A057178 Numbers k such that (12^k + 1)/13 is a prime.

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

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A082718 Numbers k such that (83*10^(k-1) + 61)/9 is a depression prime.

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