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

%I A188809 #26 Apr 03 2023 10:36:12
%S A188809 2,3,5,7,13,17,29,31,43,47,59,67,71,79,83,97,103,107,127,157,163,269,
%T A188809 271,359,383,439,457,463,487,509,547,569,571,607,643,659,683,701,709,
%U A188809 751,769,863,907,929,983,1087,1217,1303,1427,1487,2069,2371,2609,2671
%N A188809 Rigidly-deletable primes under the rule that leading zeros are disallowed.
%C A188809 Rigidly-deletable primes are deletable primes where the choice of digit to delete is unique (all other choices give nonprime numbers).
%H A188809 Arkadiusz Wesolowski, <a href="/A188809/b188809.txt">Table of n, a(n) for n = 1..10000</a>
%H A188809 Chris Caldwell, The Prime Glossary, <a href="https://t5k.org/glossary/xpage/DeletablePrime.html">Deletable prime</a>
%H A188809 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_138.htm">Puzzle 138. Deletable primes</a>, The Prime Puzzles and Problems Connection.
%e A188809 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
%t A188809 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 *)
%Y A188809 Cf. A080608 (deletable primes).
%K A188809 nonn,base
%O A188809 1,1
%A A188809 _Arkadiusz Wesolowski_, Apr 11 2011
%E A188809 Name clarified by _Arkadiusz Wesolowski_, Nov 27 2021