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A233271
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a(0)=0; thereafter a(n+1) = a(n) + 1 + number of 0's in binary representation of a(n), counted with A080791.
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29
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0, 1, 2, 4, 7, 8, 12, 15, 16, 21, 24, 28, 31, 32, 38, 42, 46, 49, 53, 56, 60, 63, 64, 71, 75, 79, 82, 87, 90, 94, 97, 102, 106, 110, 113, 117, 120, 124, 127, 128, 136, 143, 147, 152, 158, 162, 168, 174, 178, 183, 186, 190, 193, 199, 203, 207, 210, 215, 218, 222
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OFFSET
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0,3
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COMMENTS
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These are iterates of A233272: a(0)=0, and for n>0, a(n) = A233272(a(n-1)). The difference from A216431 stems from the fact that it uses A023416 to count the 0-bits in the binary expansion of n, while this sequence uses A080791, which results a slightly different start for the iteration, and a much better alignment with sequences related to "infinite trunk of binary beanstalk", A179016.
Apart from term a(2)=2, it seems that each term a(n) >= A179016(n). Please see their ratio plotted with Plot2, and also their differences: A233270.
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LINKS
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FORMULA
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a(0)=0, and for n>0, a(n) = A233272(a(n-1)).
a(0)=0, and for n>0, a(n) = a(n-1) + 1 + A080791(a(n-1)).
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MATHEMATICA
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a[0] = 0; a[n_] := a[n] = If[n == 1, 1, # + 1 + Last@ DigitCount[#, 2] &@ a[n - 1]]; Table[a@ n, {n, 0, 59}] (* or *)
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PROG
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(Scheme, with memoizing definec-macro from Antti Karttunen's IntSeq-library)
;; Alternative version:
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CROSSREFS
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Differs from A216431 only in that here 1 has been inserted into position a(1), between 0 and 2.
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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