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) = 3.66254285... (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, 15], AppendTo[lst, n]], {n, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 08 2009 *)
Select[Range@ 620, PalindromeQ@ IntegerDigits[#, 15] &] (* Michael De Vlieger, May 13 2017, Version 10.3 *)
PROG
(PARI) isok(n) = my(d=digits(n, 15)); d == Vecrev(d); \\ Michel Marcus, May 14 2017
(Python)
from sympy import integer_log
from gmpy2 import digits
def A029960(n):
if n == 1: return 0
y = 15*(x:=15**integer_log(n>>1, 15)[0])
return int((c:=n-x)*x+int(digits(c, 15)[-2::-1]or'0', 15) if n<x+y else (c:=n-y)*y+int(digits(c, 15)[-1::-1]or'0', 15)) # Chai Wah Wu, Jun 14 2024
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
STATUS
approved