1,2

Row n contains the distinct prime factors of A098550(n), in increasing order. For example, when n=13, A098550(13) = 35 and T(13,k) = [5,7].

Because A098550 is a permutation of the natural numbers, this sequence is infinite and contains every prime infinitely often.

Primes appear in order; that is, first appearance of prime(j) occurs prior to first appearance of prime(j+1).

T(n,1) = A251101(n), which are the smallest prime factors of A098550(n), n>1.

For n>1, let each coefficient in T(n,1) be prime(i). The ratio that each coefficient appears in T(j,1) {j=1..n} approaches A038110(i)/A038111(i) as j increases. For example, prime(4) = 7: as j increases, the ratio that 7 appears in T(j,1) approaches 4/105, because A038110(4)/A038111(4) = 4/105.

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.

Triangle begins T(1,1):

1

2

3

2

3

2

3 5

2 7

5

2 3

5

2 3

5 7

2

7

2 5

3 7

2 5

3

2 11

e.g., n=13: A098550(13) = 35; T(13,k) = 5,7.

Cf. A098550.

Sequence in context: A073820 A103509 A361929 * A069898 A245511 A259940

Adjacent sequences: A252938 A252939 A252940 * A252942 A252943 A252944

nonn,tabf

Bob Selcoe, Mar 22 2015

approved