

A014597


Numbers n such that n^2 is a sum of distinct factorials.


7



1, 3, 5, 11, 12, 27, 29, 71, 72, 213, 215, 603, 635, 1917, 1183893
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OFFSET

1,2


COMMENTS

If there are any terms in either A014597 or A025494 beyond the last one given (i.e., n = 1183893 in A014597; equivalently n^2 = 1401602635449 in A025494), then n^2 must be greater than 48! (about 1.24139e+61).  Jon E. Schoenfield, Aug 04 2006
A197183(a(n)) = 1.  Reinhard Zumkeller, Dec 04 2011


REFERENCES

Posting by Dan Hoey to mathfun mailing list.


LINKS

Table of n, a(n) for n=1..15.
Eric Weisstein's World of Mathematics, Factorial.


EXAMPLE

1183893^2 = 1! + 2! + 3! + 7! + 8! + 9! + 10! + 11! + 12! + 13! + 14! + 15!.
2 is not a member since 4 is not a sum of distinct factorials.


MATHEMATICA

ok[n_] := (k=1; ff={}; While[k! < n^2, AppendTo[ff, k!]; k++]; xx = Array[x, Length[ff]]; Reduce[And @@ (0 <= # <= 1 & /@ xx) && n^2 == xx.ff, xx, Integers] =!= False); ok[1] = True; Reap[Do[If[ok[n], Print[n]; Sow[n]], {n, 1, 2*10^6}]][[2, 1]] (* JeanFrançois Alcover, Jul 16 2012 *)


PROG

(Haskell)
import Data.List (elemIndices)
a014597 n = a014597_list !! (n1)
a014597_list = tail $ elemIndices 1 $ map a197183 [0..]
 Reinhard Zumkeller, Dec 04 2011


CROSSREFS

Cf. A025494, A051761, A059589.
Sequence in context: A072063 A242269 A115398 * A130603 A069977 A284795
Adjacent sequences: A014594 A014595 A014596 * A014598 A014599 A014600


KEYWORD

nonn,more,nice,changed


AUTHOR

Eric W. Weisstein


EXTENSIONS

15th term from Jud McCranie, who remarks that there no others involving terms < 21!.


STATUS

approved



