A108220 Numbers n such that concatenating n and the sum of factorials of the digits of n produces a square.

3, 102, 122, 202, 1102, 15031, 244134, 244233, 434412, 495918, 1267396, 1300035, 1324340, 1635150, 3442657, 3878374, 5064314, 6175125, 6181308, 10320734, 10560355, 10586434, 10730603, 10804230, 11544642, 16224135, 17523855

Offset

1,1

Links

Table of n, a(n) for n=1..27.

Example

495918 is in the sequence because 4!+9!+5!+9!+1!+8! = 766225 and
495918766225 = 704215^2.

Mathematica

sfdsQ[n_]:=Module[{f=Total[IntegerDigits[n]!]}, IntegerQ[ Sqrt[ n*10^IntegerLength[ f]+ f]]]; Select[Range[176*10^5], sfdsQ] (* Harvey P. Dale, Jul 06 2020 *)

Crossrefs

Cf. A061602, A109016.

Sequence in context: A069457 A142416 A110625 * A130733 A037062 A290027

Adjacent sequences: A108217 A108218 A108219 * A108221 A108222 A108223

Keyword

base,nonn

Author

Jason Earls, Jun 16 2005

Extensions

Extended by Don Reble, Nov 21 2006

Status

approved