cp's OEIS Frontend

A220161 a(n) = 1 + 2^(2^n) + 2^(2^(n+1)).

%I A220161 #49 Sep 08 2022 08:46:04
%S A220161 7,21,273,65793,4295032833,18446744078004518913,
%T A220161 340282366920938463481821351505477763073,
%U A220161 115792089237316195423570985008687907853610267032561502502920958615344897851393
%N A220161 a(n) = 1 + 2^(2^n) + 2^(2^(n+1)).
%C A220161 For n >= 1, W. Sierpiński proves that a(n) is divisible by 21.
%C A220161 For n >= 1, A. Engel shows that a(n) = a(n-1) * A220294(n-1). - _Hans Havermann_, Mar 07 2015
%D A220161 Arthur Engel, Problem-Solving Strategies, Springer, 1998, pages 121-122 (E3, said to be a "recent competition problem from the former USSR").
%D A220161 W. Sierpiński, 250 Problems in Elementary Number Theory. New York: American Elsevier, 1970. Problem #123.
%H A220161 G. C. Greubel, <a href="/A220161/b220161.txt">Table of n, a(n) for n = 0..10</a>
%H A220161 K. Zelator, <a href="http://arxiv.org/abs/0806.1514">On a theorem on sums of the form 1+2^(2^n)+2^(2^n+1)+...+2^(2^n+m) and a result linking Fermat with Mersenne numbers</a>, arXiv:0806.1514 [math.GM], 2008.
%F A220161 a(n) = A000215(n+1) + A000215(n) - 1.
%F A220161 A070969(n) = sqrt(4*a(n) - 3). a(n+1) = a(n) * (1 + a(n) - A070969(n)) = a(n) * (1 + A087046(n+2)) hence a(n) divides a(n+1). - _Michael Somos_, Dec 10 2012
%F A220161 a(n) = A002061(A000215(n)). - _Pontus von Brömssen_, Aug 31 2021
%t A220161 Table[1+2^(2^n)+2^(2^(n+1)),{n,0,7}] (* _Harvey P. Dale_, Dec 16 2015 *)
%o A220161 (Maxima) A220161(n):=1 + 2^(2^n) + 2^(2^(n+1))$ makelist(A220161(n),n,0,10); /* _Martin Ettl_, Dec 10 2012 */
%o A220161 (PARI) vector(10, n, n--; 1 + 2^(2^n) + 2^(2^(n+1))) \\ _G. C. Greubel_, Aug 10 2018
%o A220161 (Magma) [1 + 2^(2^n) + 2^(2^(n+1)): n in [0..10]]; // _G. C. Greubel_, Aug 10 2018
%o A220161 (Python)
%o A220161 def a(n): return 1 + 2**(2**n) + 2**(2**(n+1))
%o A220161 print([a(n) for n in range(8)]) # _Michael S. Branicky_, Jul 21 2021
%Y A220161 Cf. A000215, A002061, A070969, A087046, A220294, A255770, A255771, A255772.
%K A220161 nonn
%O A220161 0,1
%A A220161 _Michel Marcus_, Dec 06 2012