A318206 Numbers having no divisor d > 1 that is a binary palindrome (i.e., an element of A006995).

1, 2, 4, 8, 11, 13, 16, 19, 22, 23, 26, 29, 32, 37, 38, 41, 43, 44, 46, 47, 52, 53, 58, 59, 61, 64, 67, 71, 74, 76, 79, 82, 83, 86, 88, 89, 92, 94, 97, 101, 103, 104, 106, 109, 113, 116, 118, 121, 122, 128, 131, 134, 137, 139, 142, 143, 148, 149, 151, 152, 157

Offset

1,2

Links

Table of n, a(n) for n=1..61.

Example

The nonunit divisors of 22 are 2,11,22 and none of these are binary palindromes.

Maple

dmax:= 10: # to get all terms with at most dmax binary digits
N:= 2^dmax-1:
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:
P:= {}:
for d from 2 to dmax do
  if d::even then
    P:= P 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)};
    P:= P union B union map(`+`, B, 2^m)
  fi
od:
L:= Vector(N, 1):
for t in P  do
  L[[seq(k, k=t..N, t)]]:= 0
od:
select(t -> L[t]=1, [$1..N]); # Robert Israel, Aug 21 2018

Prog

(PARI) isok(n) = #select(x->((binary(x) == Vecrev(binary(x))) && (x>1)), divisors(n)) == 0; \\ Michel Marcus, Aug 21 2018

Crossrefs

Cf. A006995.

Sequence in context: A236206 A078649 A161607 * A022442 A308163 A056689

Adjacent sequences: A318203 A318204 A318205 * A318207 A318208 A318209

Keyword

nonn,base

Author

Jeffrey Shallit, Aug 21 2018

Status

approved