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

1,3

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.

Links

Table of n, a(n) for n=1..32.

Prog

(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

Crossrefs

Cf. A096236.

Sequence in context: A240203 A018126 A087900 * A371685 A175095 A073216

Adjacent sequences: A101213 A101214 A101215 * A101217 A101218 A101219

Keyword

nonn,base,more

Author

John W. Layman, Dec 14 2004

Extensions

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

Status

approved