A105992 Near-repunit primes.

101, 113, 131, 151, 181, 191, 211, 311, 811, 911, 1117, 1151, 1171, 1181, 1511, 1811, 2111, 4111, 8111, 10111, 11113, 11117, 11119, 11131, 11161, 11171, 11311, 11411, 16111, 101111, 111119, 111121, 111191, 111211, 111611, 112111, 113111, 131111, 311111, 511111

Offset

1,1

Comments

According to the prime glossary "a near-repunit prime is a prime all but one of whose digits are 1." This would also include {2, 3, 5, 7, 13, 17, 19, 31, 41, 61 and 71}, but this sequence only lists terms with more than two digits. - M. F. Hasler, Feb 10 2020

References

C. Caldwell and H. Dubner, "The near repunit primes 1(n-k-1)01(1k)," J. Recreational Math., 27 (1995) 35-41.

Heleen, J. P., "More near-repunit primes 1(n-k-1)D(1)1(k), D=2,3, ..., 9," J. Recreational Math., 29:3 (1998) 190-195.

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Chris Caldwell, The Top 20 Near-repdigit Primes

Chris Caldwell, The Prime Glossary, Near-repunit prime

Example

a(2)=113 is a term because 113 is a prime and all digits are 1 except one.

Mathematica

lst = {}; Do[r = (10^n - 1)/9; Do[AppendTo[lst, DeleteCases[Select[FromDigits[Permutations[Append[IntegerDigits[r], d]]], PrimeQ], r]], {d, 0, 9}], {n, 2, 14}]; Sort[Flatten[lst]] (* Arkadiusz Wesolowski, Sep 20 2011 *)

Crossrefs

Cf. A000042, A002275, A004022, A046053, A046413, A065074, A034093, A065083, A102782, A118505.

Sequence in context: A069691 A084414 A164937 * A038370 A084430 A182693

Adjacent sequences: A105989 A105990 A105991 * A105993 A105994 A105995

Keyword

base,nonn

Author

Shyam Sunder Gupta, Apr 29 2005

Status

approved