A032789 Numbers k such that (k*(k+1)*(k+2)) / (k+(k+1)+(k+2)) is a palindrome.

0, 1, 3, 4, 9, 21, 42, 99, 154, 237, 405, 999, 9999, 18991, 19291, 22021, 23587, 40293, 45072, 99999, 137652, 999999, 1278343, 1360456, 3162199, 3162499, 4029705, 4365396, 4418236, 6052891, 9999999, 31496589, 40289205, 41276535, 44295036, 56353251, 99999999

Offset

1,3

Comments

Equivalently, numbers k such that (2k + k^2)/3 is a palindrome. - Harvey P. Dale, Sep 02 2015

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

Links

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

Mathematica

palQ[n_]:=Module[{c=(2n+n^2)/3, id}, id=If[IntegerQ[c], IntegerDigits[c], {1, 2}]; id==Reverse[id]]; Select[Range[0, 10^7], palQ] (* Harvey P. Dale, Sep 02 2015 *)

Prog

(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([k for k, q in islice(agen(), 31)]) # Michael S. Branicky, Jan 24 2022

Crossrefs

Cf. A002113, A032790.

Sequence in context: A232955 A116868 A049976 * A299123 A245455 A296265

Adjacent sequences: A032786 A032787 A032788 * A032790 A032791 A032792

Keyword

nonn,base

Author

Patrick De Geest, May 15 1998

Extensions

Definition clarified by Harvey P. Dale, Sep 02 2015

a(32) and beyond from Michael S. Branicky, Jan 24 2022

Status

approved