cp's OEIS Frontend

A215511 A sequence of prime numbers expressed as minimum bases using only digits 0 and 1.

%I A215511 #9 Jul 09 2025 04:34:39
%S A215511 10,10,11,101,111,1011,10001,10011,11101,11111,11101,10011,10111,
%T A215511 101111
%N A215511 A sequence of prime numbers expressed as minimum bases using only digits 0 and 1.
%C A215511 3 = 10 base 3 = 3 + 0
%C A215511 5 = 10 base 5 = 5 + 0
%C A215511 7 = 11 base 6 = 6 + 1
%C A215511 37 = 101 base 6 = 36 + 0 + 1
%C A215511 43 = 111 base 6 = 36 + 6 + 1
%C A215511 223 = 1011 base 6 = 216 + 0 + 6 + 1
%C A215511 1297 = 10001 base 6 = 1296 + 0 + 0 + 0 + 1
%C A215511 1303 = 10011 base 6 = 1296 + 0 + 0 + 6 + 1
%C A215511 1549 = 11101 base 6 = 1296 + 216 + 36 + 0 + 1
%C A215511 2801 = 11111 base 7 = 2401 + 343 + 49 + 7 + 1
%C A215511 4673 = 11101 base 8 = 4096 + 512 + 64 + 0 + 1
%C A215511 6571 = 10011 base 9 = 6561 + 0 + 0 + 9 + 1
%C A215511 10111 = 10111 base 10 = 10000 + 0 + 100 + 10 + 1
%C A215511 101111 = 101111 base 10 = 100000 + 0 + 1000 + 100 + 10 + 1
%F A215511 Step 1: Starting at the first prime number (3), convert to the minimum base (3, as all primes may be expressed in binary).
%F A215511 Step 2: If the next prime number can be converted into the same base using only 0 and 1 without exceeding the value of the next prime number in the next base, this is the next item in the sequence.
%F A215511 Step 3: If the next prime number cannot be expressed in this base before exceeding the value of the next prime number in the next base, skip this prime number and move on to the next prime number and repeat Step 2.
%F A215511 Step 4: If the next prime number cannot be expressed in this base before exceeding the value of the next prime number in the next base, but can be expressed in the next base, this is the next item in the sequence.
%e A215511 The first term is 3 in base 3. The next prime in that base is 13, which is greater than the value of the prime in the next base, which is 5 in base 4, so the second term is 5 in base 4.
%Y A215511 A126359
%K A215511 nonn,base
%O A215511 3,1
%A A215511 _Jason Betts_, Aug 14 2012