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, 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

Robert Israel, Table of n, a(n) for n = 1..64

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

Adjacent sequences: A100550 A100551 A100552 * A100554 A100555 A100556

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