OFFSET
1,3
COMMENTS
Cilleruelo, Luca, & Baxter prove that this sequence is an additive basis of order (exactly) 3. - Charles R Greathouse IV, May 03 2020
LINKS
T. D. Noe, Table of n, a(n) for n = 1..10000
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.
Patrick De Geest, Palindromic numbers beyond base 10.
Phakhinkon Phunphayap and Prapanpong Pongsriiam, Estimates for the Reciprocal Sum of b-adic Palindromes, 2019.
FORMULA
Sum_{n>=2} 1/a(n) = 3.29797695... (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, 9], AppendTo[lst, n]], {n, 1000}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 08 2009 *)
PROG
(Python)
from gmpy2 import digits
def palQgen(l, b): # generator of palindromes in base b of length <= 2*l
if l > 0:
yield 0
for x in range(1, l+1):
for y in range(b**(x-1), b**x):
s = digits(y, b)
yield int(s+s[-2::-1], b)
for y in range(b**(x-1), b**x):
s = digits(y, b)
yield int(s+s[::-1], b)
A029955_list = list(palQgen(4, 9)) # Chai Wah Wu, Dec 01 2014
(Python)
from gmpy2 import digits
def A029955(n):
if n == 1: return 0
y = 9*(x:=9**(len(digits(n>>1, 9))-1))
return int((c:=n-x)*x+int(digits(c, 9)[-2::-1]or'0', 9) if n<x+y else (c:=n-y)*y+int(digits(c, 9)[-1::-1]or'0', 9)) # Chai Wah Wu, Jun 14 2024
(PARI) ispal(n, b=9)=my(d=digits(n, b)); d==Vecrev(d) \\ Charles R Greathouse IV, May 03 2020
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
STATUS
approved