A349031 The "Fouriest" numbers: numbers that can be expressed as a string of 4's longer than the original number in some base.

624, 3124, 6220, 15624, 37324, 78124, 78432, 223948, 390624, 549028, 1343692, 1953124, 3843200, 8062156, 9586980, 9765624, 26902404, 48372940, 48828124, 76695844, 188316832, 244140624, 290237644, 613566756, 1220703124, 1318217828, 1741425868, 4908534052

Offset

1,1

Comments

Inspired by Saturday Morning Breakfast Cereal comics.

The "Fouriest" numbers. The number shown in the comment, 624, is correctly identified as a term of the sequence.

Links

David Consiglio, Jr., Table of n, a(n) for n = 1..461

Saturday Morning Breakfast Cereal comics, Teaching math was way more fun after tenure, Feb 01 2013.

Example

624 is a member of this sequence because 624 expressed in base 5 is 4444. 4444 has 4 digits and 624 has only 3.

Prog

(Python)
from math import log
def A349031(limit):
    super_fours = []
    for length in range(4, int(log(limit, 5))+1):
        fours = "4"*length
        for base in range(5, 10):
            keep = 4*(1-base**length)//(1-base)
            if len(str(keep)) < len(fours) and keep < limit:
                super_fours.append(keep)
    return sorted(super_fours)
result = A349031(10**20)

Crossrefs

For the Fouriest transform see A268236-A268238, A268300. - N. J. A. Sloane, Nov 19 2021

Sequence in context: A216843 A043368 A158374 * A006912 A318939 A223215

Adjacent sequences: A349028 A349029 A349030 * A349032 A349033 A349034

Keyword

nonn,base

Author

David Consiglio, Jr., Nov 06 2021

Status

approved