|
|
A032789
|
|
Numbers k such that (k*(k+1)*(k+2)) / (k+(k+1)+(k+2)) is a palindrome.
|
|
2
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|