login
A029957
Numbers that are palindromic in base 12.
10
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 26, 39, 52, 65, 78, 91, 104, 117, 130, 143, 145, 157, 169, 181, 193, 205, 217, 229, 241, 253, 265, 277, 290, 302, 314, 326, 338, 350, 362, 374, 386, 398, 410, 422, 435, 447, 459, 471, 483, 495, 507, 519, 531
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
Javier Cilleruelo, Florian Luca and Lewis Baxter, Every positive integer is a sum of three palindromes, Mathematics of Computation, Vol. 87, No. 314 (2018), pp. 3023-3055, arXiv preprint, arXiv:1602.06208 [math.NT], 2017.
Phakhinkon Phunphayap and Prapanpong Pongsriiam, Estimates for the Reciprocal Sum of b-adic Palindromes, 2019.
FORMULA
Sum_{n>=2} 1/a(n) = 3.4989489... (Phunphayap and Pongsriiam, 2019). - Amiram Eldar, Oct 17 2020
MATHEMATICA
f[n_, b_]:=Module[{i=IntegerDigits[n, b]}, i==Reverse[i]]; lst={}; Do[If[f[n, 12], AppendTo[lst, n]], {n, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 08 2009 *)
PROG
(PARI) isok(n) = my(d=digits(n, 12)); d == Vecrev(d); \\ Michel Marcus, May 13 2017
(Python)
from sympy import integer_log
from gmpy2 import digits
def A029957(n):
if n == 1: return 0
y = 12*(x:=12**integer_log(n>>1, 12)[0])
return int((c:=n-x)*x+int(digits(c, 12)[-2::-1]or'0', 12) if n<x+y else (c:=n-y)*y+int(digits(c, 12)[-1::-1]or'0', 12)) # Chai Wah Wu, Jun 14 2024
CROSSREFS
Cf. A029958, A029959, A029960 (in bases 13..15).
Sequence in context: A048309 A043715 A296747 * A297277 A048323 A048336
KEYWORD
nonn,base,easy
STATUS
approved