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

Author

Bob Selcoe, Mar 22 2015

Keywords

• nonn
• tabf

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.

Examples

			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.
		

Links

• 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.

Crossrefs

Cf. A098550.