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

Author

Jeffrey Shallit, Aug 21 2018

Keywords

• nonn
• base

Examples

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

Crossrefs

Cf. A006995.

Programs

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

PARI

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