A101216 Number of n-digit base-2 deletable digit-sum multiple (DSM) integers.

1, 1, 2, 3, 5, 6, 9, 13, 26, 44, 87, 165, 305, 523, 948, 1792, 3501, 6644, 12622, 23334, 43232, 79651, 149716, 281278, 532051, 1000247, 1883093, 3577619, 6901273, 13495425, 26522993, 51976835

Offset: 1

Author

John W. Layman, Dec 14 2004

Keywords

• nonn
• base
• more

Comments

A positive integer n is a base-b digit-sum-multiple (DSM) number if the sum of the digits of n, in base b, divides n. It is a deletable base-b DSM if it has the property that removing some digit leaves either the empty string or another deletable base-b DSM.

Crossrefs

Cf. A096236.

Programs

Python

from itertools import count, islice
def ok(n, prevset):
    b = bin(n)[2:]
    if n%b.count("1"): return False
    si = (b[:i]+b[i+1:] for i in range(len(b)))
    return any(t[0] != '0' and int(t, 2) in prevset for t in si)
def agen(): # generator of terms
    s, snxt = {1}, set()
    for n in count(2):
        yield len(s)
        for i in range(2**(n-1), 2**n):
            if ok(i, s):
                snxt.add(i)
        s, snxt = snxt, set()
print(list(islice(agen(), 20))) # Michael S. Branicky, Feb 25 2023

Extensions

a(19)-a(32) from Michael S. Branicky, Feb 25 2023