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

0,3

Comments

A004086 gives the digit reversal of a number.

All positive terms belong to A070698.

This sequence is nondecreasing.

Links

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

Formula

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

Example

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

Prog

(PARI) { base = 10; k = 0; r = 0; for (n=0, 67, while (r<n, r = fromdigits(Vecrev(digits(k++, base)), base); ); print1 (k ", ")) }
(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

Crossrefs

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

Sequence in context: A262037 A262039 A354719 * A123241 A355222 A033862

Adjacent sequences: A340832 A340833 A340834 * A340836 A340837 A340838

Keyword

nonn,base

Author

Rémy Sigrist, Mar 13 2021

Status

approved