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

Author

Arkadiusz Wesolowski, Apr 11 2011

Keywords

• nonn
• base

Comments

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

Examples

			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
		

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.

Crossrefs

Cf. A080608 (deletable primes).

Programs

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 *)

Extensions

Name clarified by Arkadiusz Wesolowski, Nov 27 2021