A122954 - OEIS

A122954

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

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..n-1]));

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 A375465 A257004

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