A377463 Numbers that are not the sum of distinct powers of 4.

2, 3, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 19, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 66, 67, 70, 71, 72, 73, 74, 75, 76, 77, 78

Offset

1,1

Comments

Complement of the Moser-de Bruijn sequence (A000695).

Numbers whose base 4 digits contain either 2 or 3.

Links

Table of n, a(n) for n=1..67.

Prog

(Python)
from gmpy2 import digits
def A377463(n):
    def f(x):
        s = digits(x, 4)
        for i in range(l:=len(s)):
            if s[i]>'1':
                break
        else:
            return n+int(s, 2)
        return n-1+(int(s[:i] or '0', 2)+1<<l-i)
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m
(Python)
from itertools import count, islice
from gmpy2 import digits
def is_A377463(n): return max(digits(n, 4))>'1'
def A377463_gen(): # generator of terms
    return filter(is_A377463, count(1))
A377463_list = list(islice(A377463_gen(), 50))

Crossrefs

Cf. A000695, A074940 (base 3 analog), A136399 (base 10 analog).

Sequence in context: A225755 A126388 A039247 * A371292 A039189 A039141

Adjacent sequences: A377460 A377461 A377462 * A377464 A377465 A377466

Keyword

nonn,easy

Author

Chai Wah Wu, Oct 29 2024

Status

approved