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 A251756 a(0) = 0; for n>0, a(n) is the smallest integer not already in the list with a composite common factor with a(n-1). 2
 0, 4, 8, 12, 6, 18, 9, 27, 36, 16, 20, 10, 30, 15, 45, 54, 24, 28, 14, 42, 21, 63, 72, 32, 40, 44, 22, 66, 33, 99, 81, 90, 48, 52, 26, 78, 39, 117, 108, 56, 60, 50, 25, 75, 100, 64, 68, 34, 102, 51, 153, 126, 70, 35, 105, 84, 76, 38, 114, 57, 171, 135, 120, 80 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS It appears that this sequence includes every composite number. The values are grouped close to five lines extending from the origin with respective slope of approximately { 0.608, 0.912, 1.22, 1.82, 2.74 } = {1, 1.5, 2, 3, 4.5} * 0.608. (As in A098550 these lines are not really straight.) - M. F. Hasler, Dec 14 2014 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 David L. Applegate, Hans Havermann, Bob Selcoe, Vladimir Shevelev, N. J. A. Sloane, and Reinhard Zumkeller, The Yellowstone Permutation, arXiv preprint arXiv:1501.01669, 2015 and J. Int. Seq. 18 (2015) 15.6.7. MATHEMATICA g[a_List] := Block[{k = 4}, While[Not[CompositeQ[GCD[a[[-1]], k]]] || MemberQ[a, k], k++]; Append[a, k]]; Nest[g, {0}, 63] (* L. Edson Jeffery, Dec 08 2014 (after Robert G. Wilson v) *) PROG (PARI) invecn(v, k, x)=for(i=1, k, if(v[i]==x, return(i))); 0 alist(n)=local(v=vector(n), x, g); v[1]=4; for(k=2, n, x=4; while(invecn(v, k-1, x)||(g=gcd(v[k-1], x))==1||isprime(g), x++); v[k]=x); v (Haskell) import Data.List (delete) a251756 n = a251756_list !! (n-1) a251756_list = 0 : f 0 a002808_list where    f x zs = g zs where      g (y:ys) | d == 1 || a010051' d == 1 = g ys               | otherwise = y : f y (delete y zs)               where d = gcd x y -- Reinhard Zumkeller, Dec 08 2014 (Python) from gmpy2 import gcd, is_prime A251756_list, l, s, b = [0], 0, 1, {} for _ in range(10**3): ....i = s ....while True: ........if not i in b: ............m = gcd(i, l) ............if not (m == 1 or is_prime(m)): ................A251756_list.append(i) ................l, b[i] = i, True ................while s in b: ....................b.pop(s) ....................s += 1 ................break ........i += 1 # Chai Wah Wu, Dec 08 2014 CROSSREFS Cf. A064413, A002808, A010051, A098550. Sequence in context: A004469 A308653 A196268 * A158457 A072905 A086481 Adjacent sequences:  A251753 A251754 A251755 * A251757 A251758 A251759 KEYWORD nonn AUTHOR Franklin T. Adams-Watters, Dec 08 2014 STATUS approved

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Last modified June 15 00:00 EDT 2021. Contains 345041 sequences. (Running on oeis4.)