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A059590 Sum of distinct factorials (0! and 1! not treated as distinct). 18
0, 1, 2, 3, 6, 7, 8, 9, 24, 25, 26, 27, 30, 31, 32, 33, 120, 121, 122, 123, 126, 127, 128, 129, 144, 145, 146, 147, 150, 151, 152, 153, 720, 721, 722, 723, 726, 727, 728, 729, 744, 745, 746, 747, 750, 751, 752, 753, 840, 841, 842, 843, 846, 847, 848, 849, 864, 865 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Complement of A115945; A115944(a(n)) > 0; A115647 is a subsequence. - Reinhard Zumkeller, Feb 02 2006

A115944(a(n)) = 1. [Reinhard Zumkeller, Dec 04 2011]

From Tilman Piesk, Jun 04 2012: (Start)

The inversion vector (compare A007623) of finite permutation a(n) (compare A055089, A195663) has only zeros and ones. Interpreted as a binary number it is 2*n (or n when the inversion vector is defined without the leading 0).

The inversion set of finite permutation a(n) interpreted as a binary number (compare A211362) is A211364(n).

(End)

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..500

Index entries for sequences related to factorial numbers

FORMULA

G.f. 1/(1-x) * sum(k>=0, (k+1)!x^2^k/(1+x^2^k)). - Ralf Stephan, Jun 24 2003

a(n)=Sum_k>=0 {A030308(n,k)*A000142(k+1)}. - From Philippe Deléham, Oct 15 2011.

EXAMPLE

128 is in the sequence since 5!+3!+2!=128

MAPLE

[seq(bin2facbase(j), j=0..64)]; bin2facbase := proc(n) local i; add((floor(n/(2^i)) mod 2)*((i+1)!), i=0..floor_log_2(n)); end;

floor_log_2 := proc(n) local nn, i; nn := n; for i from -1 to n do if(0 = nn) then RETURN(i); fi; nn := floor(nn/2); od; end;

MATHEMATICA

a[n_] :=  Reverse[id = IntegerDigits[n, 2]].Range[Length[id]]!; Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Jun 19 2012, after Philippe Deléham *)

PROG

(Haskell)

import Data.List (elemIndices)

a059590 n = a059590_list !! n

a059590_list = elemIndices 1 $ map a115944 [0..]

-- Reinhard Zumkeller, Dec 04 2011

CROSSREFS

Cf. A014597, A051760, A051761, A059589, A060112 (sums of distinct non-consecutive factorials). Subset of A060132.

Other sequences that are built by replacing 2^k in the binary representation with other numbers: A029931 (naturals), A089625 (primes), A022290 (Fibonacci).

Cf. A025494 (subsequence).

Sequence in context: A003605 A132188 A060132 * A144705 A028733 A028789

Adjacent sequences:  A059587 A059588 A059589 * A059591 A059592 A059593

KEYWORD

nonn

AUTHOR

Henry Bottomley, Jan 24 2001

STATUS

approved

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Last modified October 20 04:07 EDT 2014. Contains 248329 sequences.