A050298 - OEIS

%I #10 Aug 10 2017 23:26:20

%S 2,3,5,7,11,17,13,19,31,47,29,23,59,83,127,37,41,67,149,211,307,53,43,

%T 101,167,353,499,709,61,71,103,241,401,823,1153,1613,79,73,109,257,

%U 587,937,1873,2647,3659,107,89,179,277,607,1319,2113,4201,5843,8147

%N 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.

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

%H Nathaniel Johnston, <a href="/A050298/b050298.txt">Rows n=1..20, flattened</a>

%e 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.

%e The table begins:

%e 2

%e 3  5

%e 7  11 17

%e 13 19 31 47

%e 29 23 59 83  127

%e 37 41 67 149 211 307

%e ...

%p 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

%Y Cf. A000040, A001222, A064553.

%K nonn,tabl

%O 1,1

%A _Alford Arnold_, Apr 09 2003

%E Better name and extended by _Nathaniel Johnston_, May 07 2011