A085612 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.

1, 2, 3, 4, 9, 25, 5, 7, 11, 13, 6, 10, 14, 15, 21, 8, 27, 125, 343, 1331, 2197, 12, 18, 20, 28, 44, 45, 50, 16, 81, 625, 2401, 14641, 28561, 83521, 130321, 17, 19, 23, 29, 31, 37, 41, 43, 47, 22, 26, 33, 34, 35, 38, 39, 46, 51, 55, 24, 40, 54, 56, 88, 104, 135, 136, 152

Offset

1,2

Comments

Permutation of the natural numbers when the triangle is seen flattened, inverse = A226387, see also A224401. - Reinhard Zumkeller, Jun 05 2013

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10011

Rémy Sigrist, PARI program for A085612

Index entries for sequences that are permutations of the natural numbers

Example

a(7) through a(10) = 5, 7, 11, 13 because 5 has not been used.
1;
2,3;
4,9,25;
5,7,11,13;
6,10,14,15,21;
8,27,125,343,1331,2197;
12,18,20,28,44,45,50;
16,81,625,2401,14641,28561,83521,130321;

Prog

(Haskell)
import Data.List ((\\))
a085612 n k = a085612_row n !! (k-1)
a085612_row n = a085612_tabf !! (n-1)
a085612_tabf = f 0 $ zip [1..] a046523_list where
   f x zs'@(z:zs) = (map fst ys) : f (x + 1) (zs' \\ ys) where
     ys = z : take x (filter ((== snd z) . snd) zs)
a085612_list = concat a085612_tabf
-- Reinhard Zumkeller, Jun 05 2013
(PARI) See Links section.

Crossrefs

Cf. A025487, A064839, A077558.

Cf. A085836.

Cf. A046523.

Sequence in context: A280054 A088220 A333431 * A073915 A076381 A282571

Adjacent sequences: A085609 A085610 A085611 * A085613 A085614 A085615

Keyword

nonn,tabl

Author

Alford Arnold, Jul 04 2003

Extensions

More terms from Ray Chandler, Aug 21 2003

Status

approved