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A073734
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GCD of consecutive members of the EKG sequence A064413.
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9
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1, 2, 2, 3, 3, 3, 4, 2, 5, 5, 3, 2, 7, 7, 3, 8, 4, 2, 11, 11, 3, 3, 5, 5, 7, 2, 13, 13, 3, 4, 2, 17, 17, 3, 2, 19, 19, 3, 5, 4, 2, 23, 23, 3, 2, 2, 2, 2, 7, 7, 3, 5, 5, 5, 2, 29, 29, 3, 2, 31, 31, 3, 8, 4, 2, 37, 37, 3, 3, 2, 4, 2, 41, 41, 3, 3, 7, 11, 2, 43, 43, 3, 5, 5, 5, 4, 2, 47, 47, 3, 2, 7
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OFFSET
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2,2
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COMMENTS
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All terms shown are prime powers, but this does not hold for all n. For n > 2, a(n) is divisible by A064740(n).
Based on the data of A064413, one finds that a(n) is not a prime power for 39 n's not exceeding 10000. Specifically, we have:
- a(n) = 6 for n = 968, 2236, 3330, 3496, 7773, 8957;
- a(n) = 10 for n = 579, 1221, 1428, 1604, 2092, 2872, 3048, 4434, 4697, 7355, 7448, 8923;
- a(n) = 14 for n = 9018, 2126, 8324;
- a(n) = 15 for n = 9369, 2406, 4085, 4194, 4887, 5846, 6484, 6846, 7939, 8746;
- a(n) = 20 for n = 2935, 5446, 5910, 9093;
- a(n) = 21 for n = 7468;
- a(n) = 26 for n = 1065, 5148;
- a(n) = 38 for n = 2117.
What is the first n such that a(n) = 12? And for a(n) = 18? (End)
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LINKS
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J. C. Lagarias, E. M. Rains and N. J. A. Sloane, The EKG sequence, Exper. Math. 11 (2002), 437-446; arXiv:math/0204011 [math.NT], 2002.
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FORMULA
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EXAMPLE
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a(11068) = 12 since gcd(b(11067), b(11068)) = gcd(11484, 11472) = 12,
a(58836) = 18 since gcd(b(58835), b(58836)) = gcd(60786, 60678) = 18. (End)
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MATHEMATICA
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t = {1, 2}; Join[{1}, Table[k = 3; While[MemberQ[t, k] || (y = GCD[Last[t], k]) == 1, k++]; AppendTo[t, k]; y, {91}]] (* Jayanta Basu, Jul 09 2013 *)
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PROG
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(Haskell)
a073734 n = a073734_list !! (n-2)
a073734_list = zipWith gcd a064413_list $ tail a064413_list
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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