%I
%S 1,2,3,5,7,11,13,17,23,31,37,53,71,73,1117,1123,1153,1171,1373,1723,
%T 1753,2311,2371,3137,5323,7331,11172311,11175323,11231723,11531123,
%U 11711123,11711753,13737331,17231171,17532311,23111723,23711153
%N Prime numbers (including 1) whose number of digits is a power of 2, all digits from the set {1,2,3,5,7}, such that each half of the number is already in this sequence.
%C The sequence would be tragically short were the '1' not there.
%C From _Robert Israel_, Dec 04 2019: (Start)
%C There are 5 terms with 1 digit, 9 with 2 digits, 12 with 4 digits, 15 with 8 digits, 15 with 16 digits, 7 with 32 digits, and only 1 with 64 digits, which must be the last term. (End)
%H Robert Israel, <a href="/A100553/b100553.txt">Table of n, a(n) for n = 1..64</a>
%e 11231723 is there because it is prime and 1123 and 1723 are there.
%p R[0]:= [1,2,3,5,7]:
%p for m from 1 do
%p R[m]:= select(isprime, [seq(seq(10^(2^(m1))*a+b, b=R[m1]),a=R[m1])]);
%p until R[m] = []:
%p seq(op(R[i]),i=1..m1); # _Robert Israel_, Dec 04 2019
%t L = t = {1,2,3,5,7}; While[t != {}, t = Select[FromDigits /@ Join @@@ IntegerDigits /@ Tuples[t, 2], PrimeQ]; L = Join[L, t]]; L (* _Giovanni Resta_, Dec 05 2019 *)
%K nonn,base,fini,full
%O 1,2
%A _Roger L. Bagula_, Nov 27 2004
%E Edited by _N. J. A. Sloane_, Nov 10 2005
%E Offset changed by _Robert Israel_, Dec 04 2019
