A226241 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.
89, 101, 103, 107, 109, 151, 163, 227, 251, 257, 263, 269, 281, 307, 389, 401, 409, 457, 503, 509, 521, 557, 563, 569, 587, 601, 607, 701, 709, 809, 821, 827, 857, 863, 881, 887, 907, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069
Offset: 1
Examples
All the primes < 89 can be reached from 2. For example, 2 -> 23 -> 3 -> 37.
Links
- Giovanni Resta, Table of n, a(n) for n = 1..1000
- Carlos Rivera, Puzzle 690 - Unreachable Primes
Programs
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Mathematica
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]]
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