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a(n) is the smallest even term in A098550 less than 2*prime(n) but occurring after 2*prime(n); a(n)=0 if no such term exists.
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%I #15 Mar 06 2015 22:40:13

%S 0,0,0,6,18,18,30,0,0,54,54,70,78,78,90,102,110,120,0,140,144,150,0,0,

%T 0,198,200,0,216,0,252,252,270,270,0,0,310,0,0,340,348,360,374,0,0,0,

%U 402,438,440,440,450,0,0,486,486,518,528,540,546,546,0,572,0

%N a(n) is the smallest even term in A098550 less than 2*prime(n) but occurring after 2*prime(n); a(n)=0 if no such term exists.

%C Conjecture: for n>=5, positive a(n) > prime(n). Together with the known conjecture that, for n>=26, 2*prime(n) is the first multiple of prime(n) appearing in A098550, this conjecture would easily implies that the primes in A098550 occur in the natural order.

%C (Indeed, if 101<=P<Q, then, as known, the first multiple of P, 2*P, appears earlier than the first multiple of Q, 2*Q. By the conjecture, after 2*P there cannot appear any even number <P; thus if a(n)=2*P, then a(n+2)=P appears before 2*Q.)

%H Peter J. C. Moses, <a href="/A255617/b255617.txt">Table of n, a(n) for n = 1..1000</a>

%H David L. Applegate, Hans Havermann, Bob Selcoe, Vladimir Shevelev, N. J. A. Sloane, and Reinhard Zumkeller, <a href="http://arxiv.org/abs/1501.01669">The Yellowstone Permutation</a>, arXiv preprint arXiv:1501.01669 [math.NT], 2015.

%Y Cf. A098550, A255615.

%K nonn

%O 1,4

%A _Vladimir Shevelev_, Feb 28 2015