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 A268081 Least positive integer k such that 3^n-1 and k^n-1 are relatively prime. 1
 2, 2, 2, 10, 2, 28, 2, 10, 2, 22, 10, 910, 2, 2, 2, 170, 2, 3458, 2, 110, 2, 46, 10, 910, 2, 2, 2, 290, 2, 9548, 2, 340, 10, 2, 22, 639730, 2, 2, 2, 4510, 2, 1204, 10, 230, 2, 94, 2, 216580, 2, 22, 2, 530, 2, 3458, 22, 580, 2, 118, 2, 18928910 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Note that (3^n-1)^n-1 is always relatively prime to 3^n-1. According to the conjecture given in A086892, a(n) = 2 infinitely often. When n>1, a(n) = 2 if and only if A260119(n) = 3. LINKS Table of n, a(n) for n=1..60. EXAMPLE Since 3^5-1 = 242 and 2^5-1 = 31 are relatively prime, a(5) = 3. MATHEMATICA Table[k = 1; While[! CoprimeQ[3^n - 1, k^n - 1], k++]; k, {n, 59}] (* Michael De Vlieger, Jan 27 2016 *) PROG (Sage) def min_k(n): g, k=2, 0 while g!=1: k=k+1 g=gcd(3^n-1, k^n-1) return k print([min_k(n) for n in [1..60]]) (PARI) a(n) = {k=1; while( gcd(3^n-1, k^n-1)!=1, k++); k; } CROSSREFS Cf. A086892, A260119. Sequence in context: A195706 A091185 A324956 * A319885 A368958 A125695 Adjacent sequences: A268078 A268079 A268080 * A268082 A268083 A268084 KEYWORD nonn AUTHOR Tom Edgar, Jan 25 2016 STATUS approved

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Last modified April 16 08:27 EDT 2024. Contains 371698 sequences. (Running on oeis4.)