1,1

The next entry after 72 is larger than 10^40 (if it exists). - R. J. Mathar, Jul 16 2009

2^2=1!+1!+2!. 3^2=1!+2!+3!. 6^2=3!+3!+4!. 7^2=1!+4!+4!. 29^2=1!+5!+6!. 72^2=4!+5!+7!.

s := 10^40 ; sqr := s^2 : for a from 1 do if a! > sqr then break; fi; for b from a do if a!+b! > sqr then break; fi; for c from b do if a!+b!+c! > sqr then break; fi; if issqr(a!+b!+c!) then print( sqrt(a!+b!+c!)); fi; od: od: od: # R. J. Mathar, Jul 16 2009

w := 7: f := proc (x, y, z) options operator, arrow: sqrt(factorial(x)+factorial(y)+factorial(z)) end proc: A := {}: for x to w do for y to w do for z to w do if type(f(x, y, z), integer) = true then A := `union`(A, {f(x, y, z)}) else end if end do end do end do: A; [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 03 2009]

$MaxExtraPrecision=Infinity; lst={}; Do[Do[Do[x=(a!+b!+c!)^(1/2); If[x==IntegerPart[x], AppendTo[lst, x]], {c, b, 2*4!}], {b, a, 2*4!}], {a, 2*4!}]; Union[lst]

Cf. A065433.

Sequence in context: A073317 A064731 A159069 this_sequence A070301 A065536 A088414

Adjacent sequences: A162678 A162679 A162680 this_sequence A162682 A162683 A162684

nonn

Vladimir Orlovsky (4vladimir(AT)gmail.com), Jul 10 2009

Definition rephrased by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 16 2009