cp's OEIS Frontend

A359013 Numbers k that can be written as the sum of a perfect square and a factorial in exactly 3 distinct ways.

%I A359013 #13 Dec 11 2022 10:47:26
%S A359013 145,46249,63121,42916624,18700677890064,28112213204100,
%T A359013 41654823930457982576640000,445860623276908458083942400,
%U A359013 666474080134036599385635225600
%N A359013 Numbers k that can be written as the sum of a perfect square and a factorial in exactly 3 distinct ways.
%C A359013 This does not count x^2 and (-x)^2 as distinct, nor does it count 0! and 1! as distinct.
%C A359013 a(10) > 10^30 if it exists. - _David A. Corneth_, Dec 11 2022
%e A359013 145 = 5^2 + 5! = 11^2 + 4! = 12^2 + 1!.
%o A359013 (Python) import math
%o A359013 for x in range(1, 120000000):
%o A359013     total = 0
%o A359013     prod = 1
%o A359013     factInc = 2
%o A359013     while prod <= x:
%o A359013         sq = math.sqrt(x - prod)
%o A359013         if sq % 1 == 0:
%o A359013             total = total + 1
%o A359013         prod = prod * factInc
%o A359013         factInc = factInc + 1
%o A359013     if total == 3:
%o A359013         print(x)
%Y A359013 Cf. A000142, A000290.
%Y A359013 Subset of A358071.
%K A359013 nonn,hard,more
%O A359013 1,1
%A A359013 _Walter Robinson_, Dec 11 2022
%E A359013 a(5)-a(9) from _David A. Corneth_, Dec 11 2022