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

1,2

Links

Table of n, a(n) for n=1..32.

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

Cf. A002113, A072389, A085780.

Sequence in context: A090602 A180722 A087587 * A203511 A063073 A377383

Adjacent sequences: A346916 A346917 A346918 * A346920 A346921 A346922

Keyword

nonn,base

Author

Dumitru Damian, Aug 07 2021

Extensions

More terms from Jinyuan Wang, Aug 07 2021

Status

approved