A162404 a(1)=1. a(n) = a(n-1) + (the largest value among (a(1),a(2),...,a(n-1)) that when written in binary occurs as a substring in the binary representation of n).

1, 2, 3, 5, 10, 13, 16, 18, 20, 30, 35, 38, 51, 54, 57, 73, 75, 93, 96, 116, 126, 131, 136, 139, 142, 155, 168, 171, 184, 214, 217, 233, 249, 251, 286, 304, 322, 360, 363, 383, 403, 413, 423, 428, 441, 446, 451, 467, 470, 488, 539, 559, 572, 626, 639, 642, 699

Offset

1,2

Links

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

Maple

a[1]:= 1: sa[1]:= "1":
m:= 1:
for n from 2 to 1000 do
  if n > a[m] and n > m+1 then m:= m+1 fi;
  bn:= convert(convert(n, binary), string);
  for j from m by -1 to 1 do
    if StringTools[Search](sa[j], bn) <> 0 then
       a[n]:= a[n-1]+a[j];
       sa[n]:= convert(convert(a[n], binary), string);
       break
    fi
  od
od:
seq(a[n], n=1..1000); # Robert Israel, Oct 07 2015

Mathematica

a[1] = 1; a[n_] := a[n] = a[n - 1] + Max@ Select[ Table[ a@i, {i, 0, n - 1}], StringPosition[ ToString@ FromDigits@ IntegerDigits[n, 2], ToString@ FromDigits@ IntegerDigits[ #, 2]] != {} &]; Table[ a@n, {n, 57}] (* Robert G. Wilson v, Aug 17 2009 *)

Crossrefs

Cf. A162405, A162406.

Sequence in context: A289536 A022426 A005677 * A084760 A186082 A103746

Adjacent sequences: A162401 A162402 A162403 * A162405 A162406 A162407

Keyword

base,nonn

Author

Leroy Quet, Jul 02 2009

Extensions

a(13) to a(57) from Robert G. Wilson v, Aug 17 2009

Status

approved