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A059590
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Sum of distinct factorials (0! and 1! not treated as distinct).
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17
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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; internal format)
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OFFSET
| 0,3
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COMMENTS
| Complement of A115945; A115944(a(n)) > 0; A115647 is a subsequence. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 02 2006
A115944(a(n)) = 1. [Reinhard Zumkeller, Dec 04 2011]
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 0..500
Index entries for sequences related to factorial numbers
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FORMULA
| G.f. 1/(1-x) * sum(k>=0, (k+1)!x^2^k/(1+x^2^k)). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jun 24 2003
a(n)=Sum_k>=0 {A030308(n,k)*A000142(k+1)}. - From DELEHAM Philippe, Oct 15 2011.
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EXAMPLE
| 128 is in the sequence since 5!+3!+2!=128
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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;
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PROG
| (Haskell)
import Data.List (elemIndices)
a059590 n = a059590_list !! n
a059590_list = elemIndices 1 $ map a115944 [0..]
-- Reinhard Zumkeller, Dec 04 2011
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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
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KEYWORD
| nonn
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Jan 24 2001
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