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A104887 Triangle T(n,k) = (n-k+1)-th prime, read by rows. 4
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified December 3 11:24 EST 2022. Contains 358517 sequences. (Running on oeis4.)