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

2, 7, 8, 9, 11, 12, 15, 20, 21, 27, 29, 30, 32, 34, 38, 44, 50, 52, 53, 54, 55, 56, 58, 59, 60, 62, 64, 65, 68, 70, 73, 74, 77, 78, 80, 83, 85, 86, 89, 91, 95, 98, 101, 108, 109, 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

Offset

1,1

Comments

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.

Links

Anthony Sand, Table of n, a(n) for n = 1..10000

Formula

a(n) = zeropos([sequence],n).

Example

a(1) = zeropos([10...],1) = 2,
a(2) = zeropos([10,111,1000...],2) = 7,
a(3) = zeropos([10,111,1000...],3) = 8,
a(4) = zeropos([10,111,1000...],4) = 9,
a(5) = zeropos([10,111,1000,1001...],5) = 11.

Prog

(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; ); ); }

Crossrefs

Cf. A167500, A167502.

Sequence in context: A064517 A270804 A167457 * A260581 A179772 A047354

Adjacent sequences: A287512 A287513 A287514 * A287516 A287517 A287518

Keyword

nonn,base,easy

Author

Anthony Sand, May 26 2017

Status

approved