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A130062
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Nonprime numbers k such that k divides 3^((k+1)/2) - 2^((k+1)/2) - 1.
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5
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1, 21, 49, 105, 1729, 2465, 2877, 7305, 10585, 15841, 31021, 31621, 32041, 41041, 46657, 52633, 54145, 75361, 83333, 115921, 126217, 162401, 172081, 211141, 282133, 284649, 294409, 334153, 383161, 399001, 417241, 449065, 488881, 530881
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OFFSET
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1,2
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COMMENTS
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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.
Note that primes {7,179,619} are the terms of A130060 or primes in A127074.
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LINKS
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MATHEMATICA
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Select[ 2*Range[100000]-1, !PrimeQ[ # ] && Mod[ PowerMod[3, (#+1)/2, # ] - PowerMod[2, (#+1)/2, # ] - 1, # ] == 0 & ]
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CROSSREFS
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Cf. A097934 (primes p that divide 3^((p-1)/2) - 2^((p-1)/2).
Cf. A038876 (primes p such that 6 is a square mod p.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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