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

Author

Erich Friedman

Keywords

• base
• nonn

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

Examples

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

Links

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

Crossrefs

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

Programs

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

Extensions

More terms from Patrick De Geest, Oct 15 1999