cp's OEIS Frontend

A167500 List of nonzero bits in this sequence (when terms are written in binary and concatenated).

%I A167500 #10 Aug 30 2020 13:41:46
%S A167500 1,2,4,7,8,9,10,14,17,18,20,22,23,24,26,30,31,34,36,38,41,43,44,46,48,
%T A167500 49,50,51,52,56,57,59,61,62,63,64,66,67,68,69,70,71,75,77,80,83,86,87,
%U A167500 89,91,94,95,97,99,100,101,103,104,107,109,110,111,113,114,119,120,124
%N A167500 List of nonzero bits in this sequence (when terms are written in binary and concatenated).
%C A167500 Numbers are written in base 2 in the usual way, starting with the most significant bit (MSB).
%C A167500 The sequence starts at index 1 since it is a list. The sequence cannot start with a(1)=0, else the 0th bit would not be nonzero. Thus we don't have the choice of numbering the bits starting from zero, and the first bit is necessarily set (the MSB of the first term which is nonzero), i.e., a(1)=1.
%H A167500 Rémy Sigrist, <a href="/A167500/b167500.txt">Table of n, a(n) for n = 1..10000</a>
%e A167500 The term which follows a(1)=1 (cf. comment) will be nonzero and thus have a nonzero MSB, which is the bit that comes right after the initial 1, thus bit # 2 is nonzero, therefore a(2)=2.
%e A167500 This term is written 10 in base 2, so the third bit of the sequence is zero, but the 4th bit, which will follow, will be the MSB of a(3) which is nonzero, thus a(3)=4.
%e A167500 The 4th bit is followed by two zero bits (since 4 = 100[2]), but the 7th bit is the MSB of the next term, thus nonzero, and therefore a(4)=7.
%e A167500 Since 7=111[2], the 8th and 9th bits are also set, i.e., the sequence continues a(5)=8, a(6)=9, and from now on, there is always a growing number of subsequent bits already written down.
%o A167500 (PARI) a=b=[]; for(n=1,99, #b >= n & for( i=a[n-1]+1,#b, b[i] & (a=concat(a,i)) & break); #a<n & a=concat(a,#b+1); b=concat(b,binary( a[n] ))); a
%Y A167500 Cf. A167501 (the sequence of bits of this sequence), A167502 (this sequence written in binary).
%K A167500 base,nonn
%O A167500 1,2
%A A167500 _M. F. Hasler_, Nov 05 2009