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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
1, 2, 3, 5, 7, 11, 13, 17, 23, 31, 37, 53, 71, 73, 1117, 1123, 1153, 1171, 1373, 1723, 1753, 2311, 2371, 3137, 5323, 7331, 11172311, 11175323, 11231723, 11531123, 11711123, 11711753, 13737331, 17231171, 17532311, 23111723, 23711153
OFFSET
1,2
COMMENTS
The sequence would be tragically short were the '1' not there.
From Robert Israel, Dec 04 2019: (Start)
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)
LINKS
EXAMPLE
11231723 is there because it is prime and 1123 and 1723 are there.
MAPLE
R[0]:= [1, 2, 3, 5, 7]:
for m from 1 do
R[m]:= select(isprime, [seq(seq(10^(2^(m-1))*a+b, b=R[m-1]), a=R[m-1])]);
until R[m] = []:
seq(op(R[i]), i=1..m-1); # Robert Israel, Dec 04 2019
MATHEMATICA
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 *)
CROSSREFS
Sequence in context: A012884 A068669 A316412 * A175584 A216823 A293199
KEYWORD
nonn,base,fini,full
AUTHOR
Roger L. Bagula, Nov 27 2004
EXTENSIONS
Edited by N. J. A. Sloane, Nov 10 2005
Offset changed by Robert Israel, Dec 04 2019
STATUS
approved