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

Author

David Consiglio, Jr., Nov 06 2021

Keywords

• nonn
• base

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.

Examples

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

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.

Crossrefs

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

Programs

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)