A252941 Irregular triangle T(n,k) read by rows: T(1,1) = 1, otherwise row n lists the prime factors of A098550(n), with duplicates omitted.

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, 3, 13, 11, 13, 3, 11, 2, 13, 3, 5, 2, 7, 3, 13, 2, 17, 2, 3, 5, 17, 2, 3, 5, 11, 2, 17, 5, 13, 2, 3, 7, 13, 2, 3, 5, 7, 2, 19, 3, 7, 19, 2, 3, 7, 5, 19, 2, 11

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..77.

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.

Example

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.

Crossrefs

Cf. A098550.

Sequence in context: A073820 A103509 A361929 * A069898 A245511 A259940

Adjacent sequences: A252938 A252939 A252940 * A252942 A252943 A252944

Keyword

nonn,tabf

Author

Bob Selcoe, Mar 22 2015

Status

approved