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A188809 Rigidly-deletable primes under the rule that leading zeros are disallowed. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 8 14:51 EST 2022. Contains 358695 sequences. (Running on oeis4.)