A085612 - OEIS

%I #15 Apr 25 2021 03:28:57

%S 1,2,3,4,9,25,5,7,11,13,6,10,14,15,21,8,27,125,343,1331,2197,12,18,20,

%T 28,44,45,50,16,81,625,2401,14641,28561,83521,130321,17,19,23,29,31,

%U 37,41,43,47,22,26,33,34,35,38,39,46,51,55,24,40,54,56,88,104,135,136,152

%N Triangle in which the n-th row contains n numbers (beginning with the smallest unused value) that have the same prime signature as the first entry on that row.

%C Permutation of the natural numbers when the triangle is seen flattened, inverse = A226387, see also A224401. - _Reinhard Zumkeller_, Jun 05 2013

%H Rémy Sigrist, <a href="/A085612/b085612.txt">Table of n, a(n) for n = 1..10011</a>

%H Rémy Sigrist, <a href="/A085612/a085612.gp.txt">PARI program for A085612</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%e a(7) through a(10) = 5, 7, 11, 13 because 5 has not been used.

%e 1;

%e 2,3;

%e 4,9,25;

%e 5,7,11,13;

%e 6,10,14,15,21;

%e 8,27,125,343,1331,2197;

%e 12,18,20,28,44,45,50;

%e 16,81,625,2401,14641,28561,83521,130321;

%o (Haskell)

%o import Data.List ((\\))

%o a085612 n k = a085612_row n !! (k-1)

%o a085612_row n = a085612_tabf !! (n-1)

%o a085612_tabf = f 0 $ zip [1..] a046523_list where

%o    f x zs'@(z:zs) = (map fst ys) : f (x + 1) (zs' \\ ys) where

%o      ys = z : take x (filter ((== snd z) . snd) zs)

%o a085612_list = concat a085612_tabf

%o -- _Reinhard Zumkeller_, Jun 05 2013

%o (PARI) See Links section.

%Y Cf. A025487, A064839, A077558.

%Y Cf. A085836.

%Y Cf. A046523.

%K nonn,tabl

%O 1,2

%A _Alford Arnold_, Jul 04 2003

%E More terms from _Ray Chandler_, Aug 21 2003