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A100553 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. 1

%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^(m-1))*a+b, b=R[m-1]),a=R[m-1])]);

%p until R[m] = []:

%p seq(op(R[i]),i=1..m-1); # _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

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Last modified October 15 21:38 EDT 2021. Contains 348034 sequences. (Running on oeis4.)