A305409 Positive numbers that can be expressed as the product of 1 or more binary palindromes (elements of A006995).

1, 3, 5, 7, 9, 15, 17, 21, 25, 27, 31, 33, 35, 45, 49, 51, 63, 65, 73, 75, 81, 85, 93, 99, 105, 107, 119, 125, 127, 129, 135, 147, 153, 155, 165, 175, 189, 195, 217, 219, 225, 231, 243, 245, 255, 257, 273, 279, 289, 297, 313, 315, 321, 325, 341, 343, 357, 365

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..3086

Example

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).

Maple

dmax:= 10: N:= 2^dmax: # to get all terms < N
revdigs:= proc(n)
  local L, Ln, i;
  L:= convert(n, base, 2);
  Ln:= nops(L);
  add(L[i]*2^(Ln-i), i=1..Ln);
end proc:
A:= {}:
for d from 2 to dmax do
if d::even then
    A:= A union {seq(2^(d/2)*x + revdigs(x), x=2^(d/2-1)..2^(d/2)-1)}
else
    m:= (d-1)/2;
    B:={seq(2^(m+1)*x + revdigs(x), x=2^(m-1)..2^m-1)};
    A:= A union B union map(`+`, B, 2^m)
fi
od:
R:= {1}:
for b in A do
  R:= map(t -> seq(t*b^j, j=0..floor(log[b](N/t))), R)
od:
sort(convert(R, list)); # Robert Israel, Jun 01 2018

Crossrefs

Cf. A006995.

Sequence in context: A351462 A258159 A238257 * A376857 A342572 A374199

Adjacent sequences: A305406 A305407 A305408 * A305410 A305411 A305412

Keyword

nonn,base

Author

Jeffrey Shallit, May 31 2018

Status

approved