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URL: https://oeis.org/A359013

⇱ A359013 - OEIS

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A359013
Numbers k that can be written as the sum of a perfect square and a factorial in exactly 3 distinct ways.
0
145, 46249, 63121, 42916624, 18700677890064, 28112213204100, 41654823930457982576640000, 445860623276908458083942400, 666474080134036599385635225600
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
Subset of A358071.
Sequence in context: A226849 A097730 A283520 * A265439 A060720 A015081
KEYWORD
nonn,hard,more
AUTHOR
Walter Robinson, Dec 11 2022
EXTENSIONS
a(5)-a(9) from David A. Corneth, Dec 11 2022
STATUS
approved