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A287515 a(n) = position of n-th 0 when sequence is written in base 2.

%I A287515 #14 Apr 07 2020 22:06:31
%S A287515 2,7,8,9,11,12,15,20,21,27,29,30,32,34,38,44,50,52,53,54,55,56,58,59,
%T A287515 60,62,64,65,68,70,73,74,77,78,80,83,85,86,89,91,95,98,101,108,109,
%U A287515 110,114,116,120,127,128,134,136,137,138,139,140,141,143,144,145,146,147,150,151,152,154,155,157,158,159,162
%N A287515 a(n) = position of n-th 0 when sequence is written in base 2.
%C A287515 A167500 lists the positions of 1's when the sequence is written in binary. This sequence lists the positions of 0's. When written in binary, it begins 10, 111, 1000, 1001, 1011... The first 0 appears at position 2, so a(1) = 2 = 10. The second 0 appears at position 7, so a(2) = 7 = 111. The third 0 appears at position 8, so a(3) = 8 = 1000. The sequence then becomes self-generating, because entries are added to it faster than 0's are detected in it.
%H A287515 Anthony Sand, <a href="/A287515/b287515.txt">Table of n, a(n) for n = 1..10000</a>
%F A287515 a(n) = zeropos([sequence],n).
%e A287515 a(1) = zeropos([10...],1) = 2,
%e A287515 a(2) = zeropos([10,111,1000...],2) = 7,
%e A287515 a(3) = zeropos([10,111,1000...],3) = 8,
%e A287515 a(4) = zeropos([10,111,1000...],4) = 9,
%e A287515 a(5) = zeropos([10,111,1000,1001...],5) = 11.
%o A287515 (PARI) { zeroposseq()= smx=100; s=vector(smx); s[1]=2; s[2]=7; s[3]=8; si=0; dig=digits(s[1],2); di=1; i=1; dl=0; while(si<smx, d=dig[i]; dl++; if(d==0, si++; s[si]=dl; print1(dl,", "); ); i++; if(i>#dig, di++; dig=digits(s[di],2); i=1; ); ); }
%Y A287515 Cf. A167500, A167502.
%K A287515 nonn,base,easy
%O A287515 1,1
%A A287515 _Anthony Sand_, May 26 2017