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A254669
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Consider A098550(x_n)=2*prime(n). Let a(n) be number of even numbers<=2*prime(n) in A098550 in positions <=x_n.
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3
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2, 3, 5, 4, 10, 11, 16, 19, 23, 28, 28, 36, 40, 40, 46, 52, 58, 60, 67, 70, 72, 76, 83, 89, 97, 99, 102, 107, 108, 113, 126, 129, 136, 137, 149, 151, 155, 163, 167, 172, 177, 180, 190, 193, 197, 199, 207, 220, 225, 227, 231, 239, 241, 247, 252, 262, 267, 270
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OFFSET
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1,1
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COMMENTS
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Conjecture. lim a(n)/prime(n)=1, as n goes to infinity.
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LINKS
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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.
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EXAMPLE
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Let n=10, p_n=29, 2*p_n=58, 58=A098550(63).
We consider all even terms <= 58 up to the position 63. They are 2,4,8,14,6,12,16,10,20,22,26,28,32,18,24,34,36,30,38,42,44,40,50,48,52,46,56,58.
We have 28 such numbers. Thus a(10)=28.
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MATHEMATICA
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terms = 58;
f[lst_] := Block[{k = 4}, While[GCD[lst[[-2]], k] == 1 || GCD[lst[[-1]], k]>1 || MemberQ[lst, k], k++]; Append[lst, k]]; A098550 = Nest[f, {1, 2, 3}, 12 terms];
a[n_] := Module[{p, pos}, p = Prime[n]; pos = FirstPosition[A098550, 2 p][[1]]; Count[A098550[[1 ;; pos]], k_ /; EvenQ[k] && k <= 2 p]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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