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Search: id:A130062
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| A130062 |
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Nonprime n such that n divides 3^((n+1)/2) - 2^((n+1)/2) - 1. |
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+0
4
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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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COMMENT
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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(n) = {2,3,7,179,619,17807,...} = Primes p such that p^2 divides 3^p - 2^p - 1; or primes in A127074(n).
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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 such that p divides 3^((p-1)/2) - 2^((p-1)/2). Cf. A038876(n) = Primes p such that 6 is a square mod p. Cf. A127071, A127072, A127073, A127074. Cf. A130058, A130059, A130061, A130063, A130060 = Primes p such that p^2 divides 3^p - 2^p - 1; or primes in A127074(n).
Sequence in context: A020178 A141556 A147281 this_sequence A153441 A053178 A166150
Adjacent sequences: A130059 A130060 A130061 this_sequence A130063 A130064 A130065
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), May 05 2007
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EXTENSIONS
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More terms from Ryan Propper (rpropper(AT)cs.stanford.edu), Jan 07 2008
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