

A104887


Triangle T(n,k) = (nk+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
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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(nk+1); a(n) = A000040(A004736(n)).
a(n) = A000040(m), where m=(t*t+3*t+4)/2n, t=floor((1+sqrt(8*n7))/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(nk+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 !! (n1) !! (k1)
a104887_row n = a104887_tabl !! (n1)
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[nk+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



