A043269 a(n) is the sum of the digits of n-th base-10 palindrome.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 2, 4, 6, 8, 10, 12, 14, 16, 18, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 12, 13, 14, 15, 16, 17

Offset: 1

Author

Clark Kimberling

Keywords

• nonn
• easy
• base

Examples

			For n = 36, the n-th palindrome is the 36th palindrome i.e., 262. The sum of digits of 262 (in base 10) is 2 + 6 + 2 = 10 hence a(36) = 10.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002113 (base-10 palindromes).

Programs

Mathematica

Total[IntegerDigits[#]]&/@Select[Range[0,750],PalindromeQ] (* Harvey P. Dale, Feb 11 2022 *)

PARI

a(n)={my(d, i, r); r=vector(#digits(n-10^(#digits(n\11)))+#digits(n\11)); n=n-10^(#digits(n\11)); d=digits(n); for(i=1, #d, r[i]=d[i]; r[#r+1-i]=d[i]); vecsum(r)} \\ David A. Corneth, Sep 29 2023

Python

def A043269(n):
    if n == 1: return 0
    y = 10*(x:=10**(len(str(n>>1))-1))
    return int((s:=str(n-x))[-1])+(sum(int(d) for d in s[:-1])<<1) if nChai Wah Wu, Jun 13 2024

Formula

a(n) = A007953(A002113(n)). - R. J. Mathar, Jul 20 2025