

A050298


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


1



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
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OFFSET

1,1


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.


LINKS

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


EXAMPLE

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 (54+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
...


MAPLE

with(numtheory): A050298ind := proc(n, k) option remember: local f, m: if(n=k)then return 2^n1: fi: for m from procname(n1, 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


CROSSREFS

Cf. A000040, A001222, A064553.
Sequence in context: A005685 A141656 A092180 * A094751 A280409 A076805
Adjacent sequences: A050295 A050296 A050297 * A050299 A050300 A050301


KEYWORD

nonn,tabl


AUTHOR

Alford Arnold, Apr 09 2003


EXTENSIONS

Better name and extended by Nathaniel Johnston, May 07 2011


STATUS

approved



