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A305409 Positive numbers that can be expressed as the product of 1 or more binary palindromes (elements of A006995). 1
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 (list; graph; refs; listen; history; text; internal format)
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: A121820 A258159 A238257 * A180204 A006995 A163410

Adjacent sequences:  A305406 A305407 A305408 * A305410 A305411 A305412

KEYWORD

nonn,base

AUTHOR

Jeffrey Shallit, May 31 2018

STATUS

approved

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Last modified February 18 09:42 EST 2019. Contains 320249 sequences. (Running on oeis4.)