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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 (list; graph; refs; listen; history; text; internal format)
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 math-fun 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]] (* Jean-Fran├žois Alcover, Jul 16 2012 *)

PROG

(Haskell)

import Data.List (elemIndices)

a014597 n = a014597_list !! (n-1)

a014597_list = tail $ elemIndices 1 $ map a197183 [0..]

-- Reinhard Zumkeller, Dec 04 2011

CROSSREFS

Cf. A025494, A059589, A051761.

Sequence in context: A072063 A242269 A115398 * A130603 A069977 A284795

Adjacent sequences:  A014594 A014595 A014596 * A014598 A014599 A014600

KEYWORD

nonn,more,nice

AUTHOR

Eric W. Weisstein

EXTENSIONS

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

STATUS

approved

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Last modified April 27 10:41 EDT 2017. Contains 285512 sequences.