cp's OEIS Frontend

A080943 Numbers having exactly two divisors that are also suffixes in binary representation.

%I A080943 #15 Jun 21 2023 06:46:24
%S A080943 3,5,6,7,9,10,11,12,13,14,17,18,19,20,21,22,23,24,25,26,28,29,31,33,
%T A080943 34,35,36,37,38,40,41,42,43,44,46,47,48,49,50,52,53,55,56,57,58,59,61,
%U A080943 62,65,66,67,68,69,70,71,72,73,74,76,77,79,80,81,82,83,84,86,88,89,91,92
%N A080943 Numbers having exactly two divisors that are also suffixes in binary representation.
%C A080943 A080942(a(n))=2, the two divisors are n and 1 for odd numbers and 2 for even numbers.
%H A080943 Reinhard Zumkeller, <a href="/A080943/b080943.txt">Table of n, a(n) for n = 1..10000</a>
%o A080943 (Haskell)
%o A080943 a080943 n = a080943_list !! (n-1)
%o A080943 a080943_list = filter ((== 2) . a080942) [1..]
%o A080943 -- _Reinhard Zumkeller_, Mar 27 2014
%o A080943 (Python)
%o A080943 from itertools import count, islice
%o A080943 from sympy import divisors
%o A080943 def A080943_gen(startvalue=3): # generator of terms >= startvalue
%o A080943     return filter(lambda n:(m:=n&-n)!=n and all(d==m or d==n or (d^n)&((1<<d.bit_length())-1) for d in divisors(n,generator=True)),count(max(startvalue,3)))
%o A080943 A080943_list = list(islice(A080943_gen(),20)) # _Chai Wah Wu_, Jun 20 2023
%Y A080943 Cf. A080945, A080944, A007088, A080940, A080941.
%K A080943 nonn,base
%O A080943 1,1
%A A080943 _Reinhard Zumkeller_, Feb 25 2003