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A037126
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Triangle T(n,k) = prime(k) for k = 1..n.
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10
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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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.
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FORMULA
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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
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EXAMPLE
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Triangle begins:
..... 2
.... 2,3
... 2,3,5
.. 2,3,5,7
. 2,3,5,7,11
...
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MAPLE
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T:=(n, k)->ithprime(k): seq(seq(T(n, k), k=1..n), n=1..13); # Muniru A Asiru, Mar 16 2019
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn,tabl
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AUTHOR
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Vasiliy Danilov (danilovv(AT)usa.net), Jun 15 1998
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STATUS
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approved
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