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%I A179707 #21 Jun 27 2024 22:16:11
%S A179707 4,9,25,49,121,169,289,341,361,529,731,841,961,1333,1369,1387,1681,
%T A179707 1727,1849,2047,2209,2701,2809,3277,3481,3503,3721,3763,4033,4369,
%U A179707 4489,4681,5041,5329,5461,6241,6889,7921,7957,8321,9409,9509,10201,10261,10609,10669,11449,11881
%N A179707 Semiprimes p*q such that 2^p mod q == 2^q mod p.
%C A179707 The square of every prime is here, as are the semiprimes in A179839.
%H A179707 Amiram Eldar, <a href="/A179707/b179707.txt">Table of n, a(n) for n = 1..10000</a>
%e A179707 341 is a term because 341 = 11*31 and 2^11 mod 31 = 2^31 mod 11.
%t A179707 fQ[n_] := Block[{fi = Flatten[ Table[ First@ #, {Last@ #}] & /@ FactorInteger@ n]}, Length@ fi == 2 && PowerMod[2, fi[[2]], fi[[1]]] == PowerMod[2, fi[[1]], fi[[2]]]]; Select[ Range@ 12000, fQ]
%t A179707 With[{nn=50},Take[Union[Times@@@Select[Tuples[Prime[Range[2nn]],2], PowerMod[ 2,#[[1]],#[[2]]]==PowerMod[2,#[[2]],#[[1]]]&]],nn]] (* _Harvey P. Dale_, Sep 03 2015 *)
%Y A179707 Cf. A001358, A001567.
%K A179707 nonn
%O A179707 1,1
%A A179707 _Juri-Stepan Gerasimov_, Jan 10 2011

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