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Search: id:A059590
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| A059590 |
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Sum of distinct factorials (0! and 1! not treated as distinct). |
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+0
12
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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; listen)
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OFFSET
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0,3
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COMMENT
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Complement of A115945; A115944(a(n)) > 0; A115647 is a subsequence. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 02 2006
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FORMULA
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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
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EXAMPLE
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128 is in the sequence since 5!+3!+2!=128
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MAPLE
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[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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CROSSREFS
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Cf. A014597, A051760, A051761, A059589.
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).
Sequence in context: A003605 A132188 A060132 this_sequence A144705 A028733 A028789
Adjacent sequences: A059587 A059588 A059589 this_sequence A059591 A059592 A059593
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Jan 24 2001
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