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

Author

Gary W. Adamson, Mar 29 2005

Keywords

• nonn
• tabl

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

Examples

			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;
		

Links

• Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened
• Boris Putievskiy, Transformations Integer Sequences And Pairing Functions, arXiv:1212.2732 [math.CO], 2012.

Crossrefs

Reflected triangle of A037126.

Cf. A098012 (partial products per row).

Programs

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

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

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 *)

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

Extensions

Edited by Ralf Stephan, Apr 05 2009