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Search: id:A115647
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| A115647 |
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Triangular numbers that are sums of distinct factorials. |
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+0
3
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OFFSET
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1,2
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COMMENT
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Factorials 0! and 1! are not considered distinct.
A115944(a(n)) > 0; subsequence of A059590. - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Feb 02 2006
If there are any terms beyond 40279800 they must be larger than 48!. - Jon Schoenfield, Aug 04 2006
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EXAMPLE
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1 = T(1) = 1!.
3 = T(2) = 2!+1!.
6 = T(3) = 3!.
120 = T(15) = 5!.
153 = T(17) = 5!+4!+3!+2!+1!.
5886 = T(108) = 7!+6!+5!+3!.
40470 = T(284) = 8!+5!+4!+3!.
41041 = T(286) = 8!+6!+1!.
40279800 = T(8975) = 11!+9!+5!.
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MATHEMATICA
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triQ[n_] := IntegerQ@Sqrt[8n+1]; fac=Reverse@Range[21]!; lst={}; Do[ n = Plus@@(fac*IntegerDigits[k, 2, 21]); If[triQ[n], AppendTo[lst, n]; Print[{n, k}]], {k, 2^21-1}]; Union@lst
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CROSSREFS
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Cf. A025494.
Sequence in context: A082980 A046488 A074880 this_sequence A019437 A083149 A068375
Adjacent sequences: A115644 A115645 A115646 this_sequence A115648 A115649 A115650
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KEYWORD
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nonn
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AUTHOR
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Giovanni Resta (g.resta(AT)iit.cnr.it), Jan 27 2006
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