A104887 Triangle T(n,k) = (n-k+1)-th prime, read by rows.

2, 3, 2, 5, 3, 2, 7, 5, 3, 2, 11, 7, 5, 3, 2, 13, 11, 7, 5, 3, 2, 17, 13, 11, 7, 5, 3, 2, 19, 17, 13, 11, 7, 5, 3, 2, 23, 19, 17, 13, 11, 7, 5, 3, 2, 29, 23, 19, 17, 13, 11, 7, 5, 3, 2, 31, 29, 23, 19, 17, 13, 11, 7, 5, 3, 2, 37, 31, 29, 23, 19, 17, 13, 11, 7, 5, 3, 2, 41, 37, 31, 29

Offset

1,1

Comments

Repeatedly writing the prime sequence backwards.

Sequence B is called a reverse reluctant sequence of sequence A, if B is triangle array read by rows: row number k lists first k elements of the sequence A in reverse order. Sequence A104887 is the reverse reluctant sequence of sequence the prime numbers (A000040). - Boris Putievskiy, Dec 13 2012

Links

Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

Boris Putievskiy, Transformations Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012.

Formula

T(n,k) = A000040(n-k+1); a(n) = A000040(A004736(n)).

a(n) = A000040(m), where m=(t*t+3*t+4)/2-n, t=floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Dec 13 2012

Example

Triangle begins:
   2;
   3,  2;
   5,  3,  2;
   7,  5,  3,  2;
  11,  7,  5,  3,  2;
  13, 11,  7,  5,  3,  2;
  17, 13, 11,  7,  5,  3,  2;

Maple

T:=(n, k)->ithprime(n-k+1): seq(seq(T(n, k), k=1..n), n=1..13); # Muniru A Asiru, Mar 16 2019

Mathematica

Module[{nn=15, prms}, prms=Prime[Range[nn]]; Table[Reverse[Take[prms, n]], {n, nn}]]//Flatten (* Harvey P. Dale, Aug 10 2021 *)

Prog

(Haskell)
import Data.List (inits)
a104887 n k = a104887_tabl !! (n-1) !! (k-1)
a104887_row n = a104887_tabl !! (n-1)
a104887_tabl = map reverse $ tail $ inits a000040_list
-- Reinhard Zumkeller, Oct 02 2014
(GAP) P:=Filtered([1..200], IsPrime);;
T:=Flat(List([1..13], n->List([1..n], k->P[n-k+1]))); # Muniru A Asiru, Mar 16 2019

Crossrefs

Reflected triangle of A037126.

Cf. A098012 (partial products per row).

Sequence in context: A331962 A302170 A049805 * A064886 A029600 A169616

Adjacent sequences: A104884 A104885 A104886 * A104888 A104889 A104890

Keyword

nonn,tabl

Author

Gary W. Adamson, Mar 29 2005

Extensions

Edited by Ralf Stephan, Apr 05 2009

Status

approved