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 A037126 Triangle T(n,k) = prime(k) for k = 1..n. 9
 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, 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, 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Or, triangle read by rows in which row n lists first n primes. 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 LINKS Reinhard Zumkeller, Rows n = 1..100 of triangle, flattened Boris Putievskiy, Transformations [Of] Integer Sequences And Pairing Functions, arXiv preprint arXiv:1212.2732 [math.CO], 2012. FORMULA 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 EXAMPLE Triangle begins: ..... 2 .... 2,3 ... 2,3,5 .. 2,3,5,7 . 2,3,5,7,11 ... MAPLE T:=(n, k)->ithprime(k): seq(seq(T(n, k), k=1..n), n=1..13); # Muniru A Asiru, Mar 16 2019 MATHEMATICA Flatten[ Table[ Prime[ i], {n, 12}, {i, n}]] (* Robert G. Wilson v, Aug 18 2005 *) Module[{nn=15, prs}, prs=Prime[Range[nn]]; Table[Take[prs, n], {n, nn}]]// Flatten (* Harvey P. Dale, May 02 2017 *) PROG (Haskell) a037126 n k = a037126_tabl !! (n-1) !! (k-1) a037126_row n = a037126_tabl !! (n-1) a037126_tabl = map (`take` a000040_list) [1..] -- Reinhard Zumkeller, Oct 01 2012 (GAP) P:=Filtered([1..200], IsPrime);; T:=Flat(List([1..13], n->List([1..n], k->P[k]))); # Muniru A Asiru, Mar 16 2019 CROSSREFS Cf. A000040, A002260, A037126, A138139, A138140, A138143. Cf. A007504 (row sums). Sequence in context: A022467 A306894 A169614 * A080092 A164738 A126225 Adjacent sequences:  A037123 A037124 A037125 * A037127 A037128 A037129 KEYWORD nonn,tabl AUTHOR Vasiliy Danilov (danilovv(AT)usa.net), Jun 15 1998 STATUS approved

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Last modified April 14 04:41 EDT 2021. Contains 342941 sequences. (Running on oeis4.)