A250476 -id:A250476 - cp's OEIS frontend

A251722 Square array of permutations: A(row,col) = A249822(row+1, A249821(row, col)), read by antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

1, 2, 1, 3, 2, 1, 5, 3, 2, 1, 4, 4, 3, 2, 1, 8, 9, 4, 3, 2, 1, 6, 5, 5, 4, 3, 2, 1, 14, 6, 6, 5, 4, 3, 2, 1, 13, 12, 7, 6, 5, 4, 3, 2, 1, 11, 7, 8, 7, 6, 5, 4, 3, 2, 1, 7, 8, 14, 8, 7, 6, 5, 4, 3, 2, 1, 23, 19, 9, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 10, 10, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 17, 17, 21, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 18, 42, 11, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1

Offset: 1

Antti Karttunen, Dec 07 2014

These are the "first differences" between permutations of array A249822, in a sense that by composing the first k rows of this array [from right to left, as in a(n) = row_k(...(row_2(row_1(n))))], one obtains row k+1 of A249822.

On row n the first non-fixed term is A250474(n+1) at position A250474(n), i.e., on row 1 it is 5 at n=4, on row 2 it is 9 at n=5, on row 3 it is 14 at n=9, etc. All the previous A250473(n) terms are fixed.

			The top left corner of the array:
1, 2, 3, 5, 4, 8, 6, 14, 13, 11, 7, 23, 9, 17, 18, 41, 10, 38, 12, 32, ...
1, 2, 3, 4, 9, 5, 6, 12, 7, 8, 19, 10, 17, 42, 11, 13, 22, 26, 14, 29, ...
1, 2, 3, 4, 5, 6, 7, 8, 14, 9, 10, 21, 11, 12, 13, 15, 33, 16, 25, 17, ...
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 28, 14, 15, 16, 17, 18, 19, ...
...

Inverse permutations can be found from array A251721.
Row 1: A048673, Row 2: A249746, Row 3: A250476.
Cf. A000027, A002260, A004736, A078898, A083221, A246277, A246278, A249821, A249822, A250473, A250474.

(define (A251722bi row col) (A249822bi (+ row 1) (A249821bi row col)))
(define (A251722 n) (A251722bi (A002260 n) (A004736 n)))
;; Code for A249821bi and A249822bi given in A249821, A249822.

A(row,col) = A249822(row+1, A249821(row, col)).

A(row,col) = A078898(A246278(row+1, A246277(A083221(row, col)))).

A249823 Permutation of natural numbers: a(n) = A246277(A084967(n)).

Original entry on oeis.org

1, 2, 3, 5, 7, 11, 13, 17, 4, 19, 23, 6, 29, 31, 37, 41, 9, 43, 10, 47, 53, 14, 59, 61, 67, 15, 71, 73, 22, 79, 21, 26, 83, 89, 97, 101, 103, 107, 34, 33, 25, 8, 109, 113, 39, 127, 131, 35, 38, 137, 139, 46, 149, 51, 151, 157, 49, 163, 12, 167, 173, 58, 55, 179, 181, 191, 193, 57, 62, 65, 197, 74, 69, 77, 199, 211, 223, 227, 82, 229, 233, 18

Offset: 1

Antti Karttunen, Nov 06 2014

Antti Karttunen, Table of n, a(n) for n = 1..8738
Index entries for sequences that are permutations of the natural numbers

Inverse: A249824.
Row 3 of A249821.
Cf. A064216, A084967, A246277, A249745, A249825, A250476.

(define (A249823 n) (A246277 (A084967 n)))

a(n) = A246277(A084967(n)).
As a composition of other permutations:
a(n) = A064216(A249745(n)).
a(n) = A249825(A250476(n)).

A249826 Permutation of natural numbers: a(n) = A078898(A003961(A003961(A003961(2*n)))).

Original entry on oeis.org

1, 2, 3, 14, 4, 21, 5, 92, 33, 25, 6, 144, 7, 32, 39, 641, 8, 226, 9, 170, 50, 36, 10, 1007, 46, 43, 355, 223, 11, 267, 12, 4482, 56, 55, 59, 1582, 13, 58, 68, 1190, 15, 350, 16, 249, 420, 70, 17, 7043, 78, 316, 86, 301, 18, 2485, 66, 1555, 91, 77, 19, 1869, 20, 81, 549, 31374, 80, 391, 22, 379, 109, 413, 23, 11068, 24, 88, 496, 406, 87, 473, 26, 8324, 3905, 99, 27

Offset: 1

Antti Karttunen, Dec 06 2014

nonn

Antti Karttunen, Table of n, a(n) for n = 1..127
Index entries for sequences that are permutations of the natural numbers

Inverse: A249825.
Row 4 of A249822.
Cf. A003961, A251722, A048673, A078898, A246278, A249824, A249746, A250476.

(define (A249826 n) (A078898 (A003961 (A003961 (A003961 (* 2 n))))))

a(n) = A078898(A003961(A003961(A003961(2*n)))).
a(n) = A078898(A246278(4,n)).
As a composition of other permutations:
a(n) = A250476(A249824(n)).
a(n) = A250476(A249746(A048673(n))). [Composition of the first three rows of array A251722.]

A250475 Permutation of natural numbers: a(n) = A249824(A249825(n)).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 13, 14, 15, 9, 16, 18, 20, 21, 23, 24, 12, 25, 27, 28, 19, 30, 33, 34, 35, 36, 37, 22, 17, 38, 43, 29, 44, 46, 26, 47, 50, 51, 32, 53, 55, 41, 56, 58, 60, 31, 61, 64, 65, 66, 39, 40, 67, 49, 48, 71, 75, 76, 77, 78, 80, 63, 81, 45, 84, 52, 86, 88, 90, 91, 93, 94, 62, 57, 95, 70, 69, 98, 103, 104, 105, 54, 74, 72, 106, 111, 68, 42

Offset: 1

Antti Karttunen, Dec 07 2014

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences that are permutations of the natural numbers

Inverse: A250476.
Row 3 of A251721.
Cf. A249824, A249825.

(define (A250475 n) (A249824 (A249825 n)))

a(n) = A249824(A249825(n)).

cp's OEIS Frontend

A251722 Square array of permutations: A(row,col) = A249822(row+1, A249821(row, col)), read by antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ...

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A249823 Permutation of natural numbers: a(n) = A246277(A084967(n)).

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A249826 Permutation of natural numbers: a(n) = A078898(A003961(A003961(A003961(2*n)))).

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A250475 Permutation of natural numbers: a(n) = A249824(A249825(n)).

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