A104887 - OEIS

%I #27 Feb 15 2022 12:54:12

%S 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,

%T 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,

%U 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

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

%C Repeatedly writing the prime sequence backwards.

%C 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

%H Reinhard Zumkeller, <a href="/A104887/b104887.txt">Rows n = 1..125 of triangle, flattened</a>

%H Boris Putievskiy, <a href="http://arxiv.org/abs/1212.2732">Transformations Integer Sequences And Pairing Functions</a>, arXiv:1212.2732 [math.CO], 2012.

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

%F 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

%e Triangle begins:

%e    2;

%e    3,  2;

%e    5,  3,  2;

%e    7,  5,  3,  2;

%e   11,  7,  5,  3,  2;

%e   13, 11,  7,  5,  3,  2;

%e   17, 13, 11,  7,  5,  3,  2;

%p T:=(n,k)->ithprime(n-k+1): seq(seq(T(n,k),k=1..n),n=1..13); # _Muniru A Asiru_, Mar 16 2019

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

%o (Haskell)

%o import Data.List (inits)

%o a104887 n k = a104887_tabl !! (n-1) !! (k-1)

%o a104887_row n = a104887_tabl !! (n-1)

%o a104887_tabl = map reverse $ tail $ inits a000040_list

%o -- _Reinhard Zumkeller_, Oct 02 2014

%o (GAP) P:=Filtered([1..200],IsPrime);;

%o T:=Flat(List([1..13],n->List([1..n],k->P[n-k+1]))); # _Muniru A Asiru_, Mar 16 2019

%Y Reflected triangle of A037126.

%Y Cf. A098012 (partial products per row).

%K nonn,tabl

%O 1,1

%A _Gary W. Adamson_, Mar 29 2005

%E Edited by _Ralf Stephan_, Apr 05 2009