A004151 Omit trailing zeros from n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 11, 12, 13, 14, 15, 16, 17, 18, 19, 2, 21, 22, 23, 24, 25, 26, 27, 28, 29, 3, 31, 32, 33, 34, 35, 36, 37, 38, 39, 4, 41, 42, 43, 44, 45, 46, 47, 48, 49, 5, 51, 52, 53, 54, 55, 56, 57, 58, 59, 6, 61, 62, 63, 64, 65, 66, 67, 68, 69, 7, 71, 72, 73, 74, 75, 76, 77, 78, 79, 8, 81, 82, 83, 84, 85, 86, 87, 88, 89, 9, 91, 92, 93, 94, 95, 96, 97, 98, 99, 1, 101, 102, 103, 104, 105, 106, 107, 108, 109, 11, 111, 112, 113, 114, 115, 116, 117, 118, 119, 12

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A004719, A122840.

Programs

Haskell

a004151 = until ((> 0) . (`mod` 10)) (`div` 10)
-- Reinhard Zumkeller, Feb 01 2012

Mathematica

Flatten[Table[n/Take[Intersection[Divisors[n], 10^Range[0, Floor[Log[10, n]]]], -1], {n, 120}]] (* Alonso del Arte, Feb 02 2012 *)
Table[n/10^IntegerExponent[n,10],{n,120}] (* Harvey P. Dale, May 02 2018 *)

PARI

a(n)=n/10^valuation(n,10) \\ Charles R Greathouse IV, Oct 31 2012

Python

def A004151(n):
    a, b = divmod(n,10)
    while not b:
        n = a
        a, b = divmod(n,10)
    return n # Chai Wah Wu, Feb 20 2024

Formula

a(n) = a(n/10) if n mod 10 = 0, otherwise n. - Reinhard Zumkeller, Feb 02 2012

G.f. A(x) satisfies: A(x) = A(x^10) + x/(1 - x)^2 - 10*x^10/(1 - x^10)^2. - Ilya Gutkovskiy, Oct 27 2019

Sum_{k=1..n} a(k) ~ (5/11) * n^2. - Amiram Eldar, Nov 20 2022