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) = 3.2188878... (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, 8], AppendTo[lst, n]], {n, 1000}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 08 2009 *)
PROG
(PARI) ispal(n, b=8)=my(d=digits(n, b)); d==Vecrev(d) \\ Charles R Greathouse IV, May 03 2020
(Python)
from itertools import chain, count, islice
def A029803_gen(): # generator of terms
return chain((0, ), chain.from_iterable(chain((int((s:=oct(d)[2:])+s[-2::-1], 8) for d in range(8**l, 8**(l+1))), (int((s:=oct(d)[2:])+s[::-1], 8) for d in range(8**l, 8**(l+1)))) for l in count(0)))
(Python)
def A029803(n):
if n == 1: return 0
y = (x:=1<<(m:=n.bit_length()-2)-m%3)<<3
return (c:=n-x)*x+int(oct(c)[-2:1:-1]or'0', 8) if n<x+y else (c:=n-y)*y+int(oct(c)[-1:1:-1]or'0', 8) # Chai Wah Wu, Jun 13 2024
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
STATUS
approved