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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 (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, 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

...

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

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

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Last modified March 19 19:32 EDT 2019. Contains 321330 sequences. (Running on oeis4.)