|
|
A029959
|
|
Numbers that are palindromic in base 14.
|
|
6
|
|
|
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 197, 211, 225, 239, 253, 267, 281, 295, 309, 323, 337, 351, 365, 379, 394, 408, 422, 436, 450, 464, 478, 492, 506, 520, 534, 548, 562, 576, 591
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
Cilleruelo, Luca, & Baxter prove that this sequence is an additive basis of order (exactly) 3. - Charles R Greathouse IV, May 04 2020
|
|
LINKS
|
|
|
FORMULA
|
Sum_{n>=2} 1/a(n) = 3.6112482... (Phunphayap and Pongsriiam, 2019). - Amiram Eldar, Oct 17 2020
|
|
EXAMPLE
|
195 is DD in base 14.
196 is 100 in base 14, so it's not in the sequence.
197 is 101 in base 14.
|
|
MATHEMATICA
|
palQ[n_, b_:10] := Module[{idn = IntegerDigits[n, b]}, idn == Reverse[idn]]; Select[ Range[0, 600], palQ[#, 14] &] (* Harvey P. Dale, Aug 03 2014 *)
|
|
PROG
|
(PARI) isok(n) = Pol(d=digits(n, 14)) == Polrev(d); \\ Michel Marcus, Mar 12 2017
(Python)
from sympy import integer_log
from gmpy2 import digits
if n == 1: return 0
y = 14*(x:=14**integer_log(n>>1, 14)[0])
return int((c:=n-x)*x+int(digits(c, 14)[-2::-1]or'0', 14) if n<x+y else (c:=n-y)*y+int(digits(c, 14)[-1::-1]or'0', 14)) # Chai Wah Wu, Jun 14 2024
|
|
CROSSREFS
|
Palindromes in bases 2 through 13: A006995, A014190, A014192, A029952, A029953, A029954, A029803, A029955, A002113, A029956, A029957, A029958.
|
|
KEYWORD
|
nonn,base,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|