A247358 Triangle read by rows: n-th row contains powers b^e with b + e = n + 1 in natural order.

1, 1, 2, 1, 3, 4, 1, 4, 8, 9, 1, 5, 16, 16, 27, 1, 6, 25, 32, 64, 81, 1, 7, 36, 64, 125, 243, 256, 1, 8, 49, 128, 216, 625, 729, 1024, 1, 9, 64, 256, 343, 1296, 2187, 3125, 4096, 1, 10, 81, 512, 512, 2401, 6561, 7776, 15625, 16384, 1, 11, 100, 729, 1024, 4096, 16807, 19683, 46656, 65536, 78125

Offset

1,3

Comments

Sorted rows of triangle A051129.

Links

Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

Example

.  1  |  1                            |  1^1
.  2  |  1 2                          |  1^2 2^1
.  3  |  1 3  4                       |  1^3 3^1 2^2
.  4  |  1 4  8   9                   |  1^4 4^1 2^3 3^2
.  5  |  1 5 16  16  27               |  1^5 5^1 2^4 4^2 3^3
.  6  |  1 6 25  32  64  81           |  1^6 6^1 5^2 2^5 4^3 3^4
.  7  |  1 7 36  64 125 243 256       |  1^7 7^1 6^2 2^6 5^3 3^5 4^4
.  8  |  1 8 49 128 216 625 729 1024  |  1^8 8^1 7^2 2^7 6^3 5^4 3^6 4^5 .

Mathematica

Table[Table[k^(n-k+1), {k, 1, n}] // Sort, {n, 1, 11}] // Flatten (* Jean-François Alcover, Nov 18 2019 *)

Prog

(Haskell)
import Data.List (sort)
a247358 n k = a247358_tabl !! (n-1) !! (k-1)
a247358_row n = a247358_tabl !! (n-1)
a247358_tabl = map sort a051129_tabl
(Python)
from itertools import chain
A247358_list = list(chain.from_iterable(sorted((b+1)**(n-b) for b in range(n)) for n in range(1, 8))) # Chai Wah Wu, Sep 14 2014
(PARI) row(n) = vecsort(vector(n, k, k^(n-k+1))); \\ Michel Marcus, Jan 24 2022

Crossrefs

Cf. A051129, A003101 (row sums), A247363 (central terms), A003320 (row maxima).

Sequence in context: A201634 A210211 A283054 * A297224 A180383 A133807

Adjacent sequences: A247355 A247356 A247357 * A247359 A247360 A247361

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Sep 14 2014

Status

approved