A050298 Triangle read by rows: T(n,k) = p(r), where r is the (n-k+1)-th number such that A001222(r+1) = k, and p(r) is the r-th prime.

2, 3, 5, 7, 11, 17, 13, 19, 31, 47, 29, 23, 59, 83, 127, 37, 41, 67, 149, 211, 307, 53, 43, 101, 167, 353, 499, 709, 61, 71, 103, 241, 401, 823, 1153, 1613, 79, 73, 109, 257, 587, 937, 1873, 2647, 3659, 107, 89, 179, 277, 607, 1319, 2113, 4201, 5843, 8147

Offset: 1

Author

Alford Arnold, Apr 09 2003

Keywords

• nonn
• tabl

Comments

The first column is A055003 and the main diagonal is A051438. When viewed as a sequence, this is a permutation of the prime numbers.

Examples

			a(14) = T(5,4) = p(23) = 83 because A001222(23+1) = A001222(24) = 4 since 24 has four prime factors, and this is the (5-4+1) = 2nd number with A001222 = 4.
The table begins:
2
3  5
7  11 17
13 19 31 47
29 23 59 83  127
37 41 67 149 211 307
...
		

Links

• Nathaniel Johnston, Rows n=1..20, flattened

Crossrefs

Cf. A000040, A001222, A064553.

Programs

Maple

with(numtheory): A050298ind := proc(n,k) option remember: local f,m: if(n=k)then return 2^n-1: fi: for m from procname(n-1,k)+1 do if(bigomega(m+1)=k)then return m: fi: od: end: for n from 1 to 6 do seq(ithprime(A050298ind(n,k)),k=1..n);od; # Nathaniel Johnston, May 07 2011

Extensions

Better name and extended by Nathaniel Johnston, May 07 2011