A323190 Integers k for which there exists an integer j such that s(k) + j + reversal(s(k) + j) = k where s(k) is the sum of digits of k.

0, 10, 11, 12, 14, 16, 18, 22, 33, 44, 55, 66, 77, 88, 99, 101, 110, 121, 132, 141, 143, 154, 161, 165, 176, 181, 187, 198, 201, 202, 221, 222, 241, 242, 261, 262, 281, 282, 302, 303, 322, 323, 342, 343, 362, 363, 382, 383, 403, 404, 423, 424, 443, 444, 463

Offset

1,2

Comments

Theorem: all palindromes that have an even number of digits and all palindromes that have an odd number of digits and the digit in the middle is even are in this sequence.

Links

Table of n, a(n) for n=1..55.

Viorel Niţică, Jeroz Makhania, About the Orbit Structure of Sequences of Maps of Integers, Symmetry (2019), Vol. 11, No. 11, 1374.

Example

k=10 is a term because a solution exists with j=4: s(10)=1, s(k) + j + reversal(s(k) + j) = 1 + 4 + reversal(1 + 4) = 10.

Mathematica

ok[n_] := Block[{s = Total@ IntegerDigits@ n}, Select[Range[0, n], s + # + FromDigits@ Reverse@ IntegerDigits[s + #] == n &, 1] != {}]; Select[ Range[0, 1000], ok] (* Giovanni Resta, Feb 19 2019 *)

Prog

(Java)
package com.company;
public class Main {
public static void main(String args[]) {
int counter=1;
for (int i = 0; i < 10000; i++) {
for (int j = 0; j < 10000; j++) {
int sumPlus = sumDigits(i) + j;
int check = sumPlus + reverse(sumPlus);
if (check == i) {
System.out.println(String.format("n(%d)=%d, a=%d", counter, i, j));
counter++;
break;
}
}
}
System.out.println(String.format("%d", counter));
}
public static int reverse(int x) {
String s = String.valueOf(x);
StringBuilder sb = new StringBuilder();
sb.append(s);
sb.reverse();
return Integer.parseInt(sb.toString());
}
public static int sumDigits(int x) {
int result = 0;
while (x > 0) {
result += x % 10;
x = x / 10;
}
return result;
}
}

Crossrefs

Cf. A007953 (sum of digits), A004086 (reversal).

A305130 is a subsequence.

This sequence is a subsequence of A067030.

Sequence in context: A031089 A110186 A098945 * A046431 A108697 A109279

Adjacent sequences: A323187 A323188 A323189 * A323191 A323192 A323193

Keyword

nonn,base

Author

Viorel Nitica, Jan 06 2019

Extensions

a(30)-a(55) from Giovanni Resta, Feb 19 2019

Status

approved