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Numbers having exactly two divisors that are also suffixes in binary representation.
7

%I #15 Jun 21 2023 06:46:24

%S 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 34,35,36,37,38,40,41,42,43,44,46,47,48,49,50,52,53,55,56,57,58,59,61,

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

%C A080942(a(n))=2, the two divisors are n and 1 for odd numbers and 2 for even numbers.

%H Reinhard Zumkeller, <a href="/A080943/b080943.txt">Table of n, a(n) for n = 1..10000</a>

%o (Haskell)

%o a080943 n = a080943_list !! (n-1)

%o a080943_list = filter ((== 2) . a080942) [1..]

%o -- _Reinhard Zumkeller_, Mar 27 2014

%o (Python)

%o from itertools import count, islice

%o from sympy import divisors

%o def A080943_gen(startvalue=3): # generator of terms >= startvalue

%o 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_list = list(islice(A080943_gen(),20)) # _Chai Wah Wu_, Jun 20 2023

%Y Cf. A080945, A080944, A007088, A080940, A080941.

%K nonn,base

%O 1,1

%A _Reinhard Zumkeller_, Feb 25 2003