A305409 - OEIS

%I #13 Jun 02 2018 13:09:09

%S 1,3,5,7,9,15,17,21,25,27,31,33,35,45,49,51,63,65,73,75,81,85,93,99,

%T 105,107,119,125,127,129,135,147,153,155,165,175,189,195,217,219,225,

%U 231,243,245,255,257,273,279,289,297,313,315,321,325,341,343,357,365

%N Positive numbers that can be expressed as the product of 1 or more binary palindromes (elements of A006995).

%H Robert Israel, <a href="/A305409/b305409.txt">Table of n, a(n) for n = 1..3086</a>

%e 155 is in the sequence because it is 5*31, and both 5 and 31 are palindromic numbers (with binary representations 101 and 11111, respectively).

%p dmax:= 10: N:= 2^dmax: # to get all terms < N

%p revdigs:= proc(n)

%p   local L, Ln, i;

%p   L:= convert(n, base, 2);

%p   Ln:= nops(L);

%p   add(L[i]*2^(Ln-i), i=1..Ln);

%p end proc:

%p A:= {}:

%p for d from 2 to dmax do

%p if d::even then

%p     A:= A union {seq(2^(d/2)*x + revdigs(x), x=2^(d/2-1)..2^(d/2)-1)}

%p else

%p     m:= (d-1)/2;

%p     B:={seq(2^(m+1)*x + revdigs(x), x=2^(m-1)..2^m-1)};

%p     A:= A union B union map(`+`, B, 2^m)

%p fi

%p od:

%p R:= {1}:

%p for b in A do

%p   R:= map(t -> seq(t*b^j,j=0..floor(log[b](N/t))), R)

%p od:

%p sort(convert(R,list)); # _Robert Israel_, Jun 01 2018

%Y Cf. A006995.

%K nonn,base

%O 1,2

%A _Jeffrey Shallit_, May 31 2018