A188809 Rigidly-deletable primes under the rule that leading zeros are disallowed.

2, 3, 5, 7, 13, 17, 29, 31, 43, 47, 59, 67, 71, 79, 83, 97, 103, 107, 127, 157, 163, 269, 271, 359, 383, 439, 457, 463, 487, 509, 547, 569, 571, 607, 643, 659, 683, 701, 709, 751, 769, 863, 907, 929, 983, 1087, 1217, 1303, 1427, 1487, 2069, 2371, 2609, 2671

Offset

1,1

Comments

Rigidly-deletable primes are deletable primes where the choice of digit to delete is unique (all other choices give nonprime numbers).

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000

Chris Caldwell, The Prime Glossary, Deletable prime

Carlos Rivera, Puzzle 138. Deletable primes, The Prime Puzzles and Problems Connection.

Example

103 is a member since removing a digit will either give 03 which has a leading zero, or give one of the numbers 13 or 10. 2017 is not a member since removing a digit will either give 017 which has a leading zero, or give one of the numbers 217, 207, or 201, which are all composite. - Arkadiusz Wesolowski, Nov 27 2021

Mathematica

lst1 = {}; Do[If[PrimeQ[n], p = n; Label[begin]; lst2 = {}; Do[i = IntegerDigits[p]; c = FromDigits@Drop[i, {d}]; If[Length[i] - 1 == IntegerLength[c], AppendTo[lst2, c]], {d, IntegerLength@p}]; t = Select[lst2, PrimeQ[#] &]; If[Length[t] == 1, p = FromDigits[t]; Goto[begin]]; If[IntegerLength[p] == 1, AppendTo[lst1, n]]], {n, 2671}]; lst1 (* Arkadiusz Wesolowski, Feb 22 2013 *)

Crossrefs

Cf. A080608 (deletable primes).

Sequence in context: A094947 A231474 A092621 * A350443 A152449 A048975

Adjacent sequences: A188806 A188807 A188808 * A188810 A188811 A188812

Keyword

nonn,base

Author

Arkadiusz Wesolowski, Apr 11 2011

Extensions

Name clarified by Arkadiusz Wesolowski, Nov 27 2021

Status

approved