A032790 Palindromic quotients (k*(k+1)*(k+2)) / (k+(k+1)+(k+2)).

0, 1, 5, 8, 33, 161, 616, 3333, 8008, 18881, 54945, 333333, 33333333, 120232021, 124060421, 161656161, 185464581, 541202145, 677191776, 3333333333, 6316116136, 333333333333, 544721127445, 616947749616, 3333169613333, 3333802083333, 5412843482145, 6352230322536

Offset: 1

Author

Patrick De Geest, May 15 1998

Keywords

• nonn
• base

Comments

For all i >= 1, 3^{2*i} is a term arising from k = 9^i, where ^ is repeated concatenation. - Michael S. Branicky, Jan 24 2022

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..48

Crossrefs

Cf. A032789.

Programs

Mathematica

Select[Table[Times@@Range[n,n+2]/(3n+3),{n,0,317*10^4}],PalindromeQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 06 2019 *)

Python

from itertools import count, islice
def ispal(n): s = str(n); return s == s[::-1]
def agen():
    for k in count(0):
        q, r = divmod(k*(k+2), 3)
        if r == 0 and ispal(q):
            yield k, q
print([q for k, q in islice(agen(), 31)]) # Michael S. Branicky, Jan 24 2022

Extensions

a(26) and beyond from Michael S. Branicky, Jan 24 2022