

A037126


Triangle T(n,k) = prime(k) for k = 1..n.


8



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

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, 2012.


FORMULA

As a linear array, the sequence is a(n) = A000040(m), where m = nt(t+1)/2, t=floor[(1+sqrt(8*n7))/2].  Boris Putievskiy, Dec 12 2012


EXAMPLE

Triangle begins:
..... 2
.... 2,3
... 2,3,5
.. 2,3,5,7
. 2,3,5,7,11
...


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 !! (n1) !! (k1)
a037126_row n = a037126_tabl !! (n1)
a037126_tabl = map (`take` a000040_list) [1..]
 Reinhard Zumkeller, Oct 01 2012


CROSSREFS

Cf. A000040, A138139, A138140, A138143, A002260
Cf. A007504 (row sums).
Sequence in context: A291048 A022467 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



