cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A127074 Numbers k such that k^2 divides 3^k - 2^k - 1.

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%I A127074 #18 Sep 08 2022 08:45:29
%S A127074 1,2,3,4,7,49,179,619,17807
%N A127074 Numbers k such that k^2 divides 3^k - 2^k - 1.
%C A127074 No other terms below 10^9.
%C A127074 Prime p divides 3^p - 2^p - 1. Quotients (3^p - 2^p - 1)/p are listed in A127071.
%C A127074 Numbers k such that k divides 3^k - 2^k - 1 are listed in A127072.
%C A127074 The pseudoprimes in A127072 include all powers of primes and some composite numbers that are listed in A127073.
%C A127074 Numbers k such that k^3 divides 3^k - 2^k - 1 begin 1, 4, 7 (with no other terms < 10^8).
%C A127074 Primes in {a(n)} are {2,3,7,179,619,...}.
%t A127074 Do[f=(3^n-2^n-1);If[IntegerQ[f/n^2],Print[n]],{n,1,1000}]
%t A127074 Select[Range[20000], Mod[3^# -2^# -1, #^2]==0 &] (* _G. C. Greubel_, Jan 30 2020 *)
%o A127074 (PARI) for(n=1, 20000, if((3^n-2^n-1)%n^2 == 0, print1(n", "))) \\ _G. C. Greubel_, Jan 30 2020
%o A127074 (Magma) [n: n in [1..20000] | (3^n-2^n-1) mod n^2 eq 0]; // _G. C. Greubel_, Jan 30 2020
%o A127074 (Sage) [n for n in (1..20000) if mod(3^n-2^n-1, n^2)==0 ] # _G. C. Greubel_, Jan 30 2020
%Y A127074 Cf. A127071, A127072, A127073.
%K A127074 nonn,hard,more
%O A127074 1,2
%A A127074 _Alexander Adamchuk_, Jan 04 2007
%E A127074 6 incorrect terms deleted by _D. S. McNeil_, Mar 16 2009 (the old version was 1,2,3,4,7,49,179,619,17807,95041,135433,393217,589825,1376257,1545601)
%E A127074 Edited by _Max Alekseyev_, Oct 21 2011