|
| |
|
|
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
|
| |
|
|
