A039934 Smallest k for which k, 2*k, ..., n*k all contain the digit 3.

3, 153, 1153, 1183, 3465, 7673, 7673, 7673, 65913, 65913, 65913, 76923, 232767, 232767, 232767, 232767, 232767, 2307767, 2307767, 2307767, 2307767, 3076923, 6923313, 17078903, 19507893, 56695913, 56695913, 113322666, 113322666

Offset

1,1

Comments

a(169) > 7*10^11. - Giovanni Resta, Apr 27 2017

a(169) = a(170) = ... = a(188) = 1538461526061, and a(189) > 2*10^12. - David Radcliffe, Sep 12 2018

Links

Giovanni Resta, Table of n, a(n) for n = 1..168

Example

a(2)=153 since 153 and 306 both contain a 3, and 153 is the smallest number for which this is the case.

Prog

(Python)
from itertools import count, islice
def agen(startn=1, startk=1):
    n = startn
    for k in count(startk):
        ki, nn = k, 0
        while "3" in str(ki): ki += k; nn += 1
        while n < ki//k: yield k; n += 1
print(list(islice(agen(), 22))) # Michael S. Branicky, Jul 31 2022

Crossrefs

Cf. A039932, A039933, A039935, A039936, A039937, A039938, A039939, A039940.

Sequence in context: A189248 A209393 A095225 * A378683 A156990 A075514

Adjacent sequences: A039931 A039932 A039933 * A039935 A039936 A039937

Keyword

base,nonn

Author

Erich Friedman

Extensions

More terms from Patrick De Geest, Oct 15 1999

Status

approved