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Primes that cannot be reached from 2 via a chain of primes obtained adding or deleting a digit from the end or the beginning of the previous term of the chain.
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%I #6 Jun 01 2013 03:04:09

%S 89,101,103,107,109,151,163,227,251,257,263,269,281,307,389,401,409,

%T 457,503,509,521,557,563,569,587,601,607,701,709,809,821,827,857,863,

%U 881,887,907,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069

%N Primes that cannot be reached from 2 via a chain of primes obtained adding or deleting a digit from the end or the beginning of the previous term of the chain.

%C All the primes containing a 0 are members since a 0 cannot be added at the end (it is even) nor at the beginning since, for example, 02 and 0013 are not canonical representations. The sequence is infinite, since there are exactly 820293 other primes that can be reached from 2, the largest one being 5481899436575987524681453773937333.

%H Giovanni Resta, <a href="/A226241/b226241.txt">Table of n, a(n) for n = 1..1000</a>

%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_690.htm">Puzzle 690 - Unreachable Primes</a>

%e All the primes < 89 can be reached from 2. For example, 2 -> 23 -> 3 -> 37.

%t step[p_] := Block[{dn = 10^IntegerLength@p}, Select[ Union[{Floor[p/10], Mod[p, dn/10]}, p*10 + {1, 3, 7, 9}, Range[9]*dn + p], PrimeQ[#] &]]; old = {}; new = {2}; wrk = {}; While[new != {}, wrk = Flatten[step /@ new]; old = Union[new, old]; new = Complement[wrk, old]; Print["# = ", Length@old, " max = ", Max[old], " new # = ", Length@new]]; Print["Missing up to 1000 = ", Complement[Prime@Range[168], old]]

%Y Cf. A226144, A050249.

%K nonn,base

%O 1,1

%A _Giovanni Resta_, Jun 01 2013