cp's OEIS Frontend

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

%I A318206 #15 Aug 22 2018 01:54:27
%S A318206 1,2,4,8,11,13,16,19,22,23,26,29,32,37,38,41,43,44,46,47,52,53,58,59,
%T A318206 61,64,67,71,74,76,79,82,83,86,88,89,92,94,97,101,103,104,106,109,113,
%U A318206 116,118,121,122,128,131,134,137,139,142,143,148,149,151,152,157
%N A318206 Numbers having no divisor d > 1 that is a binary palindrome (i.e., an element of A006995).
%e A318206 The nonunit divisors of 22 are 2,11,22 and none of these are binary palindromes.
%p A318206 dmax:= 10: # to get all terms with at most dmax binary digits
%p A318206 N:= 2^dmax-1:
%p A318206 revdigs:= proc(n)
%p A318206   local L, Ln, i;
%p A318206   L:= convert(n, base, 2);
%p A318206   Ln:= nops(L);
%p A318206   add(L[i]*2^(Ln-i), i=1..Ln);
%p A318206 end proc:
%p A318206 P:= {}:
%p A318206 for d from 2 to dmax do
%p A318206   if d::even then
%p A318206     P:= P union {seq(2^(d/2)*x + revdigs(x), x=2^(d/2-1)..2^(d/2)-1)}
%p A318206   else
%p A318206     m:= (d-1)/2;
%p A318206     B:={seq(2^(m+1)*x + revdigs(x), x=2^(m-1)..2^m-1)};
%p A318206     P:= P union B union map(`+`, B, 2^m)
%p A318206   fi
%p A318206 od:
%p A318206 L:= Vector(N,1):
%p A318206 for t in P  do
%p A318206   L[[seq(k,k=t..N,t)]]:= 0
%p A318206 od:
%p A318206 select(t -> L[t]=1, [$1..N]); # _Robert Israel_, Aug 21 2018
%o A318206 (PARI) isok(n) = #select(x->((binary(x) == Vecrev(binary(x))) && (x>1)), divisors(n)) == 0; \\ _Michel Marcus_, Aug 21 2018
%Y A318206 Cf. A006995.
%K A318206 nonn,base
%O A318206 1,2
%A A318206 _Jeffrey Shallit_, Aug 21 2018