cp's OEIS Frontend

A357482 a(0) = 0; for n > 0, a(n) is the smallest positive number not occurring earlier such that the binary string of the number of 1's in the binary value of a(n) + the number of 1's in the binary values of all previous terms does not appear in the binary string concatenation of a(0)..a(n-1).

%I A357482 #9 Jan 16 2023 09:10:46
%S A357482 0,1,2,3,7,4,5,63,8,6,9,16,127,11,10,12,13,14,19,511,1023,15,21,17,31,
%T A357482 18,20,22,24,25,33,23,27,26,28,35,37,38,41,1535,29,30,32,34,47,36,40,
%U A357482 55,39,43,42,45,255,46,51,383,48,44,4095,64,447,65,95,53,191,767,1791,59,49,54,57,50,52
%N A357482 a(0) = 0; for n > 0, a(n) is the smallest positive number not occurring earlier such that the binary string of the number of 1's in the binary value of a(n) + the number of 1's in the binary values of all previous terms does not appear in the binary string concatenation of a(0)..a(n-1).
%C A357482 The sequence contains large jumps in value due to some terms having to be 1 less than a power of 2 to contain sufficient 1's in their binary value to meet the term selection criteria. For example a(386) = 512, a(387) = 68719476735. See the examples below.
%e A357482 a(7) = 63 as 63 = 111111_2 which contains six 1's, the concatenation of the binary values of a(0)..a(6) is "011011111100101" which contains ten 1's, and 6 + 10 = 16 = 10000_2 which does not appear in the concatenated binary string of previous terms. All smaller unused numbers less than 63 have one to five 1's in their binary values leading to sums of 11, 12, 13, 14 or 15, but the binary values of these five sums all appear in the concatenated binary string of previous terms.
%Y A357482 Cf. A357082, A357449, A355611, A007088, A030302, A118248.
%K A357482 nonn,base
%O A357482 0,3
%A A357482 _Scott R. Shannon_, Sep 30 2022