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

1,1

Comments

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.

Links

Giovanni Resta, Table of n, a(n) for n = 1..1000

Carlos Rivera, Puzzle 690 - Unreachable Primes

Example

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

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]]

Crossrefs

Cf. A226144, A050249.

Sequence in context: A043260 A044040 A065318 * A033254 A215165 A157764

Adjacent sequences: A226238 A226239 A226240 * A226242 A226243 A226244

Keyword

nonn,base

Author

Giovanni Resta, Jun 01 2013

Status

approved