OFFSET

1,1

COMMENTS

This does not count x^2 and (-x)^2 as distinct, nor does it count 0! and 1! as distinct.

a(10) > 10^30 if it exists. - David A. Corneth, Dec 11 2022

EXAMPLE

145 = 5^2 + 5! = 11^2 + 4! = 12^2 + 1!.

PROG

(Python) import math

for x in range(1, 120000000):

total = 0

prod = 1

factInc = 2

while prod <= x:

sq = math.sqrt(x - prod)

if sq % 1 == 0:

total = total + 1

prod = prod * factInc

factInc = factInc + 1

if total == 3:

print(x)

CROSSREFS

KEYWORD

nonn,hard,more

AUTHOR

Walter Robinson, Dec 11 2022

EXTENSIONS

a(5)-a(9) from David A. Corneth, Dec 11 2022

STATUS

approved