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 A176351 Numbers n such that 2*3^n + 1 is a primitive prime factor of 10^3^n - 1. 0
 4, 180, 320, 5480, 12096, 17720, 82780, 1175232 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Consider the problem of finding the smallest number k such that the decimal representation of 1/k has period 3^e for a given e. The number k is usually 3^(e+2). However, if e is one of the n in this sequence, then the prime 2*3^n+1 is a smaller k. The first instance of these exceptions is 1/163, which has a period of 81. Subsequence of A003306. 10 must be a square residue modulo 2*3^n + 1, implying that n must be a multiple of 4. LINKS Table of n, a(n) for n=1..8. MATHEMATICA Select[Range, PrimeQ[1+2*3^# ] && MultiplicativeOrder[10, 1+2*3^# ] == 3^# &] CROSSREFS Cf. A003306 (primes of the form 2*3^n+1), A003060 (least k such that 1/k has period n). Sequence in context: A041945 A300387 A082393 * A330771 A263436 A269195 Adjacent sequences: A176348 A176349 A176350 * A176352 A176353 A176354 KEYWORD hard,more,nonn AUTHOR T. D. Noe, Apr 15 2010 EXTENSIONS Two more terms from Max Alekseyev, May 03 2010 STATUS approved

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Last modified June 9 21:43 EDT 2023. Contains 363183 sequences. (Running on oeis4.)