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%I #45 Oct 02 2020 07:24:04
%S 2,2,3,2,3,5,2,3,5,7,2,3,5,7,11,2,3,5,7,11,13,2,3,5,7,11,13,17,2,3,5,
%T 7,11,13,17,19,2,3,5,7,11,13,17,19,23,2,3,5,7,11,13,17,19,23,29,2,3,5,
%U 7,11,13,17,19,23,29,31,2,3,5,7,11,13,17,19,23,29,31,37,2,3,5,7,11,13,17
%N Triangle T(n,k) = prime(k) for k = 1..n.
%C Or, triangle read by rows in which row n lists first n primes.
%C Sequence B is called a reluctant sequence of sequence A, if B is triangle array read by rows: row number k coincides with first k elements of the sequence A. Sequence A037126 is reluctant sequence of the prime numbers A000040. - _Boris Putievskiy_, Dec 12 2012
%H Reinhard Zumkeller, <a href="/A037126/b037126.txt">Rows n = 1..100 of triangle, flattened</a>
%H Boris Putievskiy, <a href="http://arxiv.org/abs/1212.2732">Transformations [Of] Integer Sequences And Pairing Functions</a>, arXiv preprint arXiv:1212.2732 [math.CO], 2012.
%F As a linear array, the sequence is a(n) = A000040(m), where m = n-t(t+1)/2, t=floor((-1+sqrt(8*n-7))/2). - _Boris Putievskiy_, Dec 12 2012
%e Triangle begins:
%e ..... 2
%e .... 2,3
%e ... 2,3,5
%e .. 2,3,5,7
%e . 2,3,5,7,11
%e ...
%p T:=(n,k)->ithprime(k): seq(seq(T(n,k),k=1..n),n=1..13); # _Muniru A Asiru_, Mar 16 2019
%t Flatten[ Table[ Prime[ i], {n, 12}, {i, n}]] (* _Robert G. Wilson v_, Aug 18 2005 *)
%t Module[{nn=15,prs},prs=Prime[Range[nn]];Table[Take[prs,n],{n,nn}]]// Flatten (* _Harvey P. Dale_, May 02 2017 *)
%o (Haskell)
%o a037126 n k = a037126_tabl !! (n-1) !! (k-1)
%o a037126_row n = a037126_tabl !! (n-1)
%o a037126_tabl = map (`take` a000040_list) [1..]
%o -- _Reinhard Zumkeller_, Oct 01 2012
%o (GAP) P:=Filtered([1..200],IsPrime);;
%o T:=Flat(List([1..13],n->List([1..n],k->P[k]))); # _Muniru A Asiru_, Mar 16 2019
%Y Cf. A000040, A002260, A037126, A138139, A138140, A138143.
%Y Cf. A007504 (row sums).
%K nonn,tabl
%O 1,1
%A Vasiliy Danilov (danilovv(AT)usa.net), Jun 15 1998
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