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A113167 Triangle read by rows; n-th row begins with n and contains n primes greater than n and not already used.

%I A113167 #15 Jan 30 2025 16:48:50
%S A113167 0,1,2,2,3,5,3,7,11,13,4,17,19,23,29,5,31,37,41,43,47,6,53,59,61,67,
%T A113167 71,73,7,79,83,89,97,101,103,107,8,109,113,127,131,137,139,149,151,9,
%U A113167 157,163,167,173,179,181,191,193,197,10,199,211,223,227,229,233,239,241,251
%N A113167 Triangle read by rows; n-th row begins with n and contains n primes greater than n and not already used.
%C A113167 This is just the prime number sequence with the integer sequence inserted at triangular number positions. - _R. J. Mathar_, Aug 29 2007
%H A113167 Harvey P. Dale, <a href="/A113167/b113167.txt">Table of n, a(n) for n = 0..1000</a>
%H A113167 Chris Caldwell, <a href="https://t5k.org/lists/small/1000.txt">The First 1000 primes</a>.
%e A113167 0
%e A113167 1 2
%e A113167 2 3 5
%e A113167 3 7 11 13
%e A113167 4 17 19 23 29
%e A113167 5 31 37 41 43 47
%t A113167 With[{nn=10},Join[{0},Flatten[Thread[{Range[nn],TakeList[Prime[Range[(nn(nn+1))/2]],Range[nn]]}]]]] (* _Harvey P. Dale_, Jan 30 2025 *)
%Y A113167 Cf. A113031.
%K A113167 nonn,tabl,easy
%O A113167 0,3
%A A113167 _Parthasarathy Nambi_, Jan 05 2006
%E A113167 More terms from _R. J. Mathar_, Aug 29 2007