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A101216
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Number of n-digit base-2 deletable digit-sum multiple (DSM) integers.
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0
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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
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OFFSET
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1,3
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COMMENTS
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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.
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LINKS
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PROG
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(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()
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CROSSREFS
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KEYWORD
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nonn,base,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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