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A346919
Numbers that are both palindromes (A002113) and terms of A072389.
0
0, 4, 252, 2112, 2772, 6336, 21012, 27072, 42924, 48384, 48984, 63036, 252252, 297792, 407704, 2327232, 2572752, 2747472, 2774772, 2958592, 4457544, 4811184, 6378736, 6396936, 25777752, 27633672, 29344392, 63099036, 63399336, 404080404, 409757904, 441525144
OFFSET
1,2
FORMULA
Intersection of A072389 and A002113.
Intersection of 4*A085780 and A002113.
MATHEMATICA
p[n_] := n*(n + 1); m = 1000; Select[Union[ Times @@@ Tuples[p /@ Range[0, m], {2}]], # <= 2*p[m] && PalindromeQ[#] &] (* Amiram Eldar, Aug 13 2021 *)
PROG
(SageMath)
# the sequence numbers up to a limit
def a346919_upto(lim, alst=set([0])):
for i in range(1, int(lim**0.25)):
for j in range(i, int((lim/(i*(i+1)))**0.5)+1):
if all([(k:=i*(i+1)*j*(j+1))<=lim, str(k)==str(k)[::-1]]): alst.add(k)
return sorted(alst)
print(a346919_upto(10**9)) # Dumitru Damian, Apr 05 2023
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Dumitru Damian, Aug 07 2021
EXTENSIONS
More terms from Jinyuan Wang, Aug 07 2021
STATUS
approved