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

2,2

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)

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

Formula

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

Example

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)

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 *)

Prog

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

Crossrefs

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

Sequence in context: A340294 A270920 A262956 * A231335 A271237 A062558

Adjacent sequences: A073731 A073732 A073733 * A073735 A073736 A073737

Keyword

easy,nonn

Author

David Wasserman, Aug 06 2002

Status

approved