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 A101216 Number of n-digit base-2 deletable digit-sum multiple (DSM) integers. 0
 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 (list; graph; refs; listen; history; text; internal format)
 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 * A175095 A073216 A181902 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

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Last modified October 2 20:55 EDT 2023. Contains 365840 sequences. (Running on oeis4.)