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) = 2.9200482... (Phunphayap and Pongsriiam, 2019). - Amiram Eldar, Oct 17 2020
MAPLE
# test for palindrome in base b, from N. J. A. Sloane, Sep 13 2015
b:=5;
ispal := proc(n) global b; local t1, t2, i;
if n <= b-1 then return(1); fi;
t1:=convert(n, base, b); t2:=nops(t1);
for i from 1 to floor(t2/2) do
if t1[i] <> t1[t2+1-1] then return(-1); fi;
od: return(1); end;
lis:=[]; for n from 0 to 100 do if ispal(n) = 1 then lis:=[op(lis), n]; fi; od: lis;
MATHEMATICA
f[n_, b_] := Module[{i=IntegerDigits[n, b]}, i==Reverse[i]]; lst={}; Do[If[f[n, 5], AppendTo[lst, n]], {n, 1000}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 08 2009 *)
Select[Range[0, 1000], IntegerDigits[#, 5]==Reverse[IntegerDigits[#, 5]]&] (* Harvey P. Dale, Oct 24 2020 *)
PROG
(Magma) [n: n in [0..900] | Intseq(n, 5) eq Reverse(Intseq(n, 5))]; // Vincenzo Librandi, Sep 09 2015
(PARI) ispal(n, b=5)=my(d=digits(n, b)); d==Vecrev(d) \\ Charles R Greathouse IV, May 03 2020
(Python)
from gmpy2 import digits
def A029952(n):
if n == 1: return 0
y = 5*(x:=5**(len(digits(n>>1, 5))-1))
return int((c:=n-x)*x+int(digits(c, 5)[-2::-1]or'0', 5) if n<x+y else (c:=n-y)*y+int(digits(c, 5)[-1::-1]or'0', 5)) # Chai Wah Wu, Jun 13 2024
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
STATUS
approved