A077194 Smallest multiple of n with least digit sum.

1, 10, 3, 100, 10, 12, 1001, 1000, 9, 10, 11, 12, 1001, 10010, 30, 10000, 100000001, 18, 1000000001, 100, 21, 110, 100000000001, 120, 100, 10010, 27, 100100, 100000000000001, 30, 10000011, 100000, 33, 1000000010, 10010, 36, 111, 10000000010, 10101

Offset

1,2

Comments

This is not the digital root (A010888) but the digital sum (A007953).

a(2^k)=10^k.

Links

Jason Yuen, Table of n, a(n) for n = 1..2000

Prog

(Python)
def dijkstra(dist, start, startValue, traverse): ... # See A077196
def A077194(n):
    def traverse(remainder, d):
        add1, number = d
        return [((remainder*10)%n, (add1, number*10)),
                ((remainder+1)%n, (add1+1, number+1))]
    return dijkstra([(n+1, 0)]*n, 1%n, (1, 1), traverse)[0][1]  # Jason Yuen, Feb 28 2024

Crossrefs

Cf. A077195, A077196.

Sequence in context: A260680 A111126 A165790 * A038305 A089478 A028967

Adjacent sequences: A077191 A077192 A077193 * A077195 A077196 A077197

Keyword

base,nonn

Author

Amarnath Murthy, Nov 01 2002

Extensions

Edited by Robert G. Wilson v, Nov 05 2002

Corrected by Matthew Vandermast, Apr 12 2003

a(34) corrected by Max Alekseyev, Feb 26 2009

a(38) corrected by Paul Tek, Mar 14 2013

Status

approved