A130664 a(1)=1. a(n) = a(n-1) + (number of terms from among a(1) through a(n-1) which are factorials).

1, 2, 4, 6, 9, 12, 15, 18, 21, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210, 215, 220, 225, 230, 235, 240, 245, 250

Offset

1,2

Comments

Also this is an irregular array where row n contains the n! consecutive multiples of n starting with n!.

For n >= 1, (a(n), A084555(n)) = (1,1), (2,3), (4,5), (6,8), (9,11), (12,14), ... gives the starting and ending offsets of the n-th permutation in the sequences like A030298 and A030496. Gives also the fixed points of A220662; we have A220662(a(n)) = a(n). - Antti Karttunen, Dec 18 2012

Links

A. Karttunen, Rows 1..7 of irregular table, flattened.

Formula

a(n) = A084555(n-1) + 1.

Example

When interpreted as an irregular table, the rows begin as:
1;
2, 4;
6, 9, 12, 15, 18, 21;

Maple

A[1]:= 1:
nextf:= 2!:
m:= 1:
for n from 2 to 100 do
  A[n]:= A[n-1]+m;
  if A[n] = nextf then
     m:= m+1;
      nextf:= (m+1)!;
  fi;
od:
seq(A[i], i=1..100); # Robert Israel, Apr 28 2016

Mathematica

Table[Range[n!, (n + 1)! - 1, n], {n, 5}] // Flatten (* Michael De Vlieger, Aug 29 2017 *)

Prog

(Scheme): (define (A130664 n) (+ 1 (A084555(- n 1))))

Crossrefs

Cf. A000142, A084555, A220662.

Sequence in context: A328212 A352191 A256393 * A014011 A064424 A067850

Adjacent sequences: A130661 A130662 A130663 * A130665 A130666 A130667

Keyword

easy,nonn

Author

Leroy Quet, Jun 21 2007

Status

approved