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

Author

Alford Arnold, Jul 04 2003

Keywords

• nonn
• tabl

Comments

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

Examples

			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;
		

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

Crossrefs

Cf. A025487, A064839, A077558.

Cf. A085836.

Cf. A046523.

Programs

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.

Extensions

More terms from Ray Chandler, Aug 21 2003