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Nonprime numbers k such that k divides 3^((k+1)/2) - 2^((k+1)/2) - 1.
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%I #15 Sep 21 2024 03:50:08

%S 1,21,49,105,1729,2465,2877,7305,10585,15841,31021,31621,32041,41041,

%T 46657,52633,54145,75361,83333,115921,126217,162401,172081,211141,

%U 282133,284649,294409,334153,383161,399001,417241,449065,488881,530881

%N Nonprime numbers k such that k divides 3^((k+1)/2) - 2^((k+1)/2) - 1.

%C The perfect squares in listed terms are a(1) = 1, a(3) = 49 = 7^2, a(13) = 32041 = 179^2 and a(29) = 383161 = 619^2.

%C Note that primes {7,179,619} are the terms of A130060 or primes in A127074.

%H Amiram Eldar, <a href="/A130062/b130062.txt">Table of n, a(n) for n = 1..1000</a>

%t Select[ 2*Range[100000]-1, !PrimeQ[ # ] && Mod[ PowerMod[3,(#+1)/2,# ] - PowerMod[2,(#+1)/2,# ] - 1, # ] == 0 & ]

%Y Cf. A097934 (primes p that divide 3^((p-1)/2) - 2^((p-1)/2)).

%Y Cf. A038876 (primes p such that 6 is a square mod p).

%Y Cf. A127071, A127072, A127073, A127074.

%Y Cf. A130058, A130059, A130061, A130063, A130060, A127074.

%K nonn

%O 1,2

%A _Alexander Adamchuk_, May 05 2007

%E More terms from _Ryan Propper_, Jan 07 2008