%I #13 Oct 07 2015 04:01:23
%S 1,2,3,5,10,13,16,18,20,30,35,38,51,54,57,73,75,93,96,116,126,131,136,
%T 139,142,155,168,171,184,214,217,233,249,251,286,304,322,360,363,383,
%U 403,413,423,428,441,446,451,467,470,488,539,559,572,626,639,642,699
%N 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).
%H Robert Israel, <a href="/A162404/b162404.txt">Table of n, a(n) for n = 1..10000</a>
%p a[1]:= 1: sa[1]:= "1":
%p m:= 1:
%p for n from 2 to 1000 do
%p if n > a[m] and n > m+1 then m:= m+1 fi;
%p bn:= convert(convert(n,binary),string);
%p for j from m by -1 to 1 do
%p if StringTools[Search](sa[j],bn) <> 0 then
%p a[n]:= a[n-1]+a[j];
%p sa[n]:= convert(convert(a[n],binary),string);
%p break
%p fi
%p od
%p od:
%p seq(a[n],n=1..1000); # _Robert Israel_, Oct 07 2015
%t 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 *)
%Y Cf. A162405, A162406.
%K base,nonn
%O 1,2
%A _Leroy Quet_, Jul 02 2009
%E a(13) to a(57) from _Robert G. Wilson v_, Aug 17 2009