cp's OEIS Frontend

A127072 Numbers k that divide 3^k - 2^k - 1.

%I A127072 #18 Sep 08 2022 08:45:29
%S A127072 1,2,3,4,5,7,8,9,11,13,16,17,19,23,27,29,31,32,37,41,43,45,47,49,53,
%T A127072 59,61,64,67,71,73,79,81,83,89,97,101,103,107,109,113,127,128,131,137,
%U A127072 139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233
%N A127072 Numbers k that divide 3^k - 2^k - 1.
%C A127072 Prime p divides 3^p - 2^p - 1.
%C A127072 Quotients (3^p - 2^p - 1)/p, where p is prime, are listed in A127071.
%C A127072 Pseudoprimes in a(n) include all powers of primes {2,3,7} and some composite numbers that are listed in A127073.
%C A127072 Numbers k such that k^2 divides 3^k - 2^k - 1 are listed in A127074.
%C A127072 Numbers k such that k^3 divides 3^k - 2^k - 1 are {1, 4, 7, ...}.
%H A127072 G. C. Greubel, <a href="/A127072/b127072.txt">Table of n, a(n) for n = 1..10000</a>
%t A127072 Select[Range[1000],IntegerQ[(3^#-2^#-1)/# ]&]
%o A127072 (PARI) is(n)=Mod(3,n)^n-Mod(2,n)^n==1 \\ _Charles R Greathouse IV_, Nov 04 2016
%o A127072 (Magma) [n: n in [1..250] | ((3^n - 2^n - 1) mod n) eq 0]; // _G. C. Greubel_, Aug 12 2019
%o A127072 (Sage) [n for n in (1..250) if mod(3^n-2^n-1, n)==0 ] # _G. C. Greubel_, Jan 30 2020
%Y A127072 Cf. A127071, A127073, A127074.
%K A127072 nonn
%O A127072 1,2
%A A127072 _Alexander Adamchuk_, Jan 04 2007