A340835 a(n) is the least k such that the digit reversal of k is greater than or equal to n.

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

Offset: 0

Author

Rémy Sigrist, Mar 13 2021

Keywords

• nonn
• base

Comments

A004086 gives the digit reversal of a number.

All positive terms belong to A070698.

This sequence is nondecreasing.

Examples

			For n = 1000:
- A004086(k) < 1000 for any k <= 1000,
- A004086(1001) = 1001 >= 1000,
- so a(1000) = 1001.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A004086, A070698, A340836 (binary analog).

Programs

PARI

{ base = 10; k = 0; r = 0; for (n=0, 67, while (r
				

Python

def A340835(n):
    if n == 0:
        return 0
    s = str(n)
    for i, x in enumerate(s):
        if x != '9':
            break
    else:
        return n
    s1, s2 = s[:i+1], s[i+1:]
    if s2 == '':
        if s1[-1] == '0':
            return int(str(n+1)[::-1])
        else:
            return int(s[::-1])
    if int(s2) <= 1:
        return int('1'+s2[-2::-1]+s1[::-1])
    else:
        return int('1'+'0'*(len(s2)-1)+str(int(s1)+1)[::-1]) # Chai Wah Wu, Mar 14 2021

Formula

a(n) <= n + 1 with equality iff n = 10^k for some k > 0.