A224929 Primes such that concatenation of two adjacent terms and two adjacent digits is also prime.

2, 3, 7, 19, 73, 1117, 31, 37, 97, 373, 13, 1171, 11131, 11113, 79, 71713, 17137, 11173, 11719, 717979, 71719, 731173, 111373, 11197, 313, 71971, 11731, 13171, 11119, 731737, 113719, 719731, 379, 737119, 797119, 7171111, 37117, 19717, 11311, 97117, 17971

Offset

1,1

Comments

Conjecture: all prime congruent to 1 (mod 3) which only have the odd digits {1, 3, 7, 9} but not 5 eventually appear. So far 139, 193, 199, 331, 337, 397, 733, 739, 919, 937, 991, 997, etc. have not appeared. - Robert G. Wilson v, May 06 2014

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..600 (first 345 terms from Lars Blomberg)

Formula

a(n) is the smallest prime not yet used which fits the conditions.

Example

a(6)=1117 because it is a prime, 731117 is a prime, 31, 11, 11 and 17 are prime and no smaller and as-yet-unused prime satisfies the conditions.

Mathematica

f[s_List] := Block[{id, p = s[[-1]], q = 3}, While[ pq = p*10^Floor[1 + Log10@ q] + q; id = IntegerDigits@ pq; Union@ Join[{1, 3, 7, 9}, id] != {1, 3, 7, 9} || MemberQ[s, q] || Union@ PrimeQ[ Join[ {pq}, FromDigits@# & /@ Partition[id, 2, 1]]] != {True}, q = NextPrime@ q]; Append[s, q]]; Nest[f, {2, 3}, 39] (* Robert G. Wilson v, May 06 2014 *)

Crossrefs

Cf. A242190.

Sequence in context: A358049 A025563 A336296 * A110887 A065060 A164625

Adjacent sequences: A224926 A224927 A224928 * A224930 A224931 A224932

Keyword

nonn,base

Author

Lars Blomberg, inspired by Eric Angelini, Apr 20 2013

Status

approved