A346919 Numbers that are both palindromes (A002113) and terms of A072389.

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

Author

Dumitru Damian, Aug 07 2021

Keywords

• nonn
• base

Crossrefs

Cf. A002113, A072389, A085780.

Programs

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 *)

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

Formula

Intersection of A072389 and A002113.

Intersection of 4*A085780 and A002113.

Extensions

More terms from Jinyuan Wang, Aug 07 2021