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.

A179839 Semiprimes p*q with p < q and 2^p (mod q) == 2^q (mod p).

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%I A179839 #18 Jun 06 2025 17:03:59
%S A179839 341,731,1333,1387,1727,2047,2701,3277,3503,3763,4033,4369,4681,5461,
%T A179839 7957,8321,9509,10261,10669,13747,14491,15709,17557,17861,18721,19147,
%U A179839 19951,20737,23377,31417,31609,31621,35333,42799,43921,44669,46979,49141,49901,49981
%N A179839 Semiprimes p*q with p < q and 2^p (mod q) == 2^q (mod p).
%C A179839 The semiprime super-Poulet numbers (semiprimes in A050217) are a subsequence.
%H A179839 Amiram Eldar, <a href="/A179839/b179839.txt">Table of n, a(n) for n = 1..10000</a>
%t A179839 aQ[n_] := Module[{f = FactorInteger[n]}, If[Length[f] == 2 && f[[1, 2]] == f[[2, 2]] == 1, p = f[[1, 1]]; q = f[[2, 1]], Return[False]]; PowerMod[2, p, q] == PowerMod[2, q, p]]; Select[Range[50000], aQ] (* _Amiram Eldar_, Oct 23 2019 *)
%t A179839 Take[Times@@@Select[Tuples[Prime[Range[350]],2],#[[1]]!=#[[2]]&&PowerMod[2,#[[1]],#[[2]]]==PowerMod[2,#[[2]],#[[1]]]&]//Union,40] (* _Harvey P. Dale_, Jun 06 2025 *)
%Y A179839 Cf. A006881, A179707 (which allows p = q).
%K A179839 nonn
%O A179839 1,1
%A A179839 _T. D. Noe_, Jan 10 2011