A255617 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.

0, 0, 0, 6, 18, 18, 30, 0, 0, 54, 54, 70, 78, 78, 90, 102, 110, 120, 0, 140, 144, 150, 0, 0, 0, 198, 200, 0, 216, 0, 252, 252, 270, 270, 0, 0, 310, 0, 0, 340, 348, 360, 374, 0, 0, 0, 402, 438, 440, 440, 450, 0, 0, 486, 486, 518, 528, 540, 546, 546, 0, 572, 0

Offset

1,4

Comments

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.

(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.)

Links

Peter J. C. Moses, Table of n, a(n) for n = 1..1000

David L. Applegate, Hans Havermann, Bob Selcoe, Vladimir Shevelev, N. J. A. Sloane, and Reinhard Zumkeller, The Yellowstone Permutation, arXiv preprint arXiv:1501.01669 [math.NT], 2015.

Crossrefs

Cf. A098550, A255615.

Sequence in context: A252897 A174904 A074390 * A253771 A223218 A077630

Adjacent sequences: A255614 A255615 A255616 * A255618 A255619 A255620

Keyword

nonn

Author

Vladimir Shevelev, Feb 28 2015

Status

approved