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
KEYWORD
nonn,base
AUTHOR
Lars Blomberg, inspired by Eric Angelini, Apr 20 2013
STATUS
approved