

A122954


a(1) = 1. a(n) = number of earlier terms which, when written in binary, are substrings of binary n.


2



1, 1, 2, 3, 3, 5, 4, 4, 5, 5, 8, 7, 8, 6, 5, 7, 7, 5, 7, 10, 9, 11, 15, 10, 9, 13, 13, 12, 17, 11, 9, 7, 7, 8, 11, 8, 13, 11, 16, 16, 15, 10, 17, 18, 18, 21, 22, 15, 15, 14, 12, 19, 18, 19, 24, 22, 20, 24, 25, 21, 25, 17, 14, 11, 11, 11, 13, 12, 17, 16, 21, 15, 11, 19, 26, 17, 23, 22, 24
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,3


COMMENTS

First occurrence of k: 1, 3, 4, 7, 6, 14, 12, 11, 21, 20, 22, 28, 26, 50, 23, 39, 29, 44, 52, 57, 46, 47, 77, 55, 59, ...


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


EXAMPLE

Binary a(1) = 1, binary a(2) = 1, binary a(3) = 10, binary a(7) = 100 and binary a(8) = 100 are all substrings of binary 9 = 1001. So a(9) = 5.


MAPLE

A[1]:= 1:
S[1]:= "1":
for n from 2 to 100 do
B:= convert(convert(n, binary), string);
A[n]:= nops(select(t > SearchText(S[t], B)>0, [$1..n1]));
S[n]:= convert(convert(A[n], binary), string);
od:
seq(A[i], i=1..100); # Robert Israel, Apr 11 2019


MATHEMATICA

f[ s_ ] := Append[ s, Length@ Select[ s, StringPosition[ ToString@ FromDigits@ IntegerDigits[ Length@s + 1, 2 ], ToString@ FromDigits@ IntegerDigits[ #, 2 ] ] != {} & ] ]; Nest[ f, {1}, 79 ] (* Robert G. Wilson v, Nov 01 2006 *)


CROSSREFS

Sequence in context: A167494 A091238 A178047 * A268087 A257004 A126571
Adjacent sequences: A122951 A122952 A122953 * A122955 A122956 A122957


KEYWORD

nonn,look


AUTHOR

Leroy Quet, Oct 25 2006


EXTENSIONS

More terms from Robert G. Wilson v, Nov 01 2006


STATUS

approved



