A084556 -id:A084556 - cp's OEIS frontend

A220660 Irregular table, where the n-th row consists of numbers 0..(n!-1).

0, 0, 1, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39

Offset: 1

Antti Karttunen, Dec 18 2012

Used for computing A030298: a(n) tells the zero-based ranking of the n-th permutation in A030298 (A030299(n)) in the lexicographical ordering of all finite permutations of the same size.

			Rows of this irregular table begin as:
0;
0, 1;
0, 1, 2, 3, 4, 5;

Antti Karttunen, The rows 1..7 of the irregular table, flattened.

Cf. A220661, A030298.

Table[Range[0,n!-1],{n,5}]//Flatten (* Harvey P. Dale, Feb 27 2017 *)

(define (A220660 n) (- n (A007489 (-1+ (A084556 n))) 1))

a(n) = n - A007489(A084556(n)-1) - 1.

a(n) = A220661(n)-1.

A236857 Each n occurs the least common multiple (LCM) of {1, 2, ..., n} (= A003418(n)) times.

Original entry on oeis.org

0, 1, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6

Offset: 0

Antti Karttunen, Feb 27 2014

Least k such that A236856(k) >= n.
Zero occurs once at a(0), because A003418(0)=1 by definition.
Useful when computing irregular tables like A238280, as a(n) gives the row index of the n-th term in such sequences. Note that as A238280 begins with row 1, it starts referring to this sequence only from a(1)=1 onward.

			Can be viewed as an irregular table, where each row n (starting from row zero) contains A003418(n) copies of n:
0;
1;
2, 2;
3, 3, 3, 3, 3, 3;
4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4;
...

Antti Karttunen, Rows 0..10 of the table, flattened

Cf. A003418, A084556, A236856, A236858.

Join[{0},Flatten[Table[PadRight[{},LCM@@Range[n],{n}],{n,6}]]] (* Harvey P. Dale, Jul 29 2021 *)

A220661 Irregular table, where the n-th row consists of numbers 1..n!

Original entry on oeis.org

1, 1, 2, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39

Offset: 1

Antti Karttunen, Dec 18 2012

			Rows of this irregular table begin as:
1;
1, 2;
1, 2, 3, 4, 5, 6;

Antti Karttunen, The rows 1..7 of the irregular table, flattened.

Cf. A000142, A220660.

Flatten[Range[#]&/@(Range[5]!)] (* Harvey P. Dale, Apr 20 2013 *)

(define (A220661 n) (- n (A007489 (-1+ (A084556 n)))))

a(n) = n - A007489(A084556(n)-1).

a(n) = A220660(n)+1.

cp's OEIS Frontend

A220660 Irregular table, where the n-th row consists of numbers 0..(n!-1).

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A236857 Each n occurs the least common multiple (LCM) of {1, 2, ..., n} (= A003418(n)) times.

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Author

Keywords

Comments

Examples

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Mathematica

A220661 Irregular table, where the n-th row consists of numbers 1..n!

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Scheme

Formula