A064419 a(n) = n for n <= 5; for n > 5, a(n) = smallest number not already used such that gcd(a(n), a(n-1)) >= 5.
1, 2, 3, 4, 5, 10, 15, 20, 25, 30, 6, 12, 18, 9, 27, 36, 24, 8, 16, 32, 40, 35, 7, 14, 21, 28, 42, 48, 54, 45, 50, 55, 11, 22, 33, 44, 66, 60, 65, 13, 26, 39, 52, 78, 72, 56, 49, 63, 70, 75, 80, 64, 88, 77, 84, 90, 81, 99, 108, 96, 102, 17, 34, 51, 68, 85, 95, 19, 38, 57, 76, 114, 120
Offset: 1
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
- J. C. Lagarias, E. M. Rains and N. J. A. Sloane, The EKG sequence, Exper. Math. 11 (2002), 437-446.
- Index entries for sequences related to EKG sequence
- Index entries for sequences that are permutations of the natural numbers
Programs
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Haskell
a064419 n = a064419_list !! (n-1) a064419_list = [1,2,3,4,5] ++ f 5 [] [6..] where f z xs (y:ys) | y `gcd` z > 4 = y : f y [] (reverse xs ++ ys) | otherwise = f z (y:xs) ys -- Reinhard Zumkeller, Sep 17 2001 -
Mathematica
Module[{gcdlist=Range[5],k},Do[k=6;While[GCD[k,Last[gcdlist]]<5 || MemberQ[ gcdlist,k],k++];AppendTo[gcdlist,k];,{80}];gcdlist] (* Harvey P. Dale, Apr 11 2012 *) -
Python
from sympy import gcd l=list(range(1, 6)) for n in range(5, 101): k=6 while k in l or gcd(l[n - 1], k)<5: k+=1 l.append(k) print(l) # Indranil Ghosh, Jun 27 2017
Extensions
More terms from Naohiro Nomoto, Sep 30 2001
Comments