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
KEYWORD
nonn,tabl
AUTHOR
Vasiliy Danilov (danilovv(AT)usa.net), Jun 15 1998
STATUS
approved