A073734 GCD of consecutive members of the EKG sequence A064413.

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

Offset: 2

Author

David Wasserman, Aug 06 2002

Keywords

• easy
• nonn

Comments

All terms shown are prime powers, but this does not hold for all n. For n > 2, a(n) is divisible by A064740(n).

The GCD of A064413(578)=620 and A064413(579)=610 is 10. This is the first time the GCD is not a prime-power. - N. J. A. Sloane, Mar 30 2015

a(A064955(n)) = A000040(n) for n > 1. [Reinhard Zumkeller, Sep 17 2001]

From Jianing Song, Sep 27 2023: (Start)

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)

Examples

			a(8) = 4 because gcd(A064413(7), A064413(8)) = gcd(12, 8) = 4.
From _Michael De Vlieger_, Sep 27 2023: (Start)
Let b(n) = A064413(n):
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)
		

Links

• Jianing Song, Table of n, a(n) for n = 2..10000 (based on the data of A064413; terms n = 2..1000 from T. D. Noe)
• 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.
• Index entries for sequences related to EKG sequence

Crossrefs

Cf. A064413, A064740, A073735, A380506, A382222, A382271.

Programs

Haskell

a073734 n = a073734_list !! (n-2)
a073734_list = zipWith gcd a064413_list $ tail a064413_list
-- Reinhard Zumkeller, Sep 17 2001

Mathematica

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 *)

Formula

a(n) = gcd(A064413(n-1), A064413(n)).