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
John Cerkan, 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) = 3.4369816... (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, 11], AppendTo[lst, n]], {n, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 08 2009 *)
pal11Q[n_]:=Module[{idn11=IntegerDigits[n, 11]}, idn11==Reverse[idn11]]; Select[Range[0, 500], pal11Q] (* Harvey P. Dale, May 11 2015 *)
Select[Range[0, 500], PalindromeQ[IntegerDigits[#, 11]] &] (* Michael De Vlieger, May 12 2017, Version 10.3 *)
PROG
(PARI) ispal(n, b)=my(tmp, d=log(n+.5)\log(b)-1); while(d, tmp=n%b; n\=b; if(n\b^d!=tmp, return(0)); n=n%(b^d); d-=2; ); d<0||n%(b+1)==0
is(n)=ispal(n, 11) \\ Charles R Greathouse IV, Aug 21 2012
(PARI) ispal(n, b=11)=my(d=digits(n, b)); d==Vecrev(d) \\ Charles R Greathouse IV, May 04 2020
(Sage)
[n for n in (0..499) if Word(n.digits(11)).is_palindrome()] # Peter Luschny, Sep 13 2018
(Python)
from gmpy2 import digits
from sympy import integer_log
def A029956(n):
if n == 1: return 0
y = 11*(x:=11**integer_log(n>>1, 11)[0])
return int((c:=n-x)*x+int(digits(c, 11)[-2::-1]or'0', 11) if n<x+y else (c:=n-y)*y+int(digits(c, 11)[-1::-1]or'0', 11)) # Chai Wah Wu, Jun 14 2024
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
STATUS
approved