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A055938
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Integers not generated by b(n) = b(floor(n/2)) + n (cf. A005187).
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84
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2, 5, 6, 9, 12, 13, 14, 17, 20, 21, 24, 27, 28, 29, 30, 33, 36, 37, 40, 43, 44, 45, 48, 51, 52, 55, 58, 59, 60, 61, 62, 65, 68, 69, 72, 75, 76, 77, 80, 83, 84, 87, 90, 91, 92, 93, 96, 99, 100, 103, 106, 107, 108, 111, 114, 115, 118, 121, 122, 123, 124, 125, 126, 129
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OFFSET
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1,1
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COMMENTS
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Note that the lengths of the consecutive runs in a(n) form sequence A001511.
Integers that are not a sum of distinct integers of the form 2^k-1. - Vladeta Jovovic, Jan 24 2003
Also n! never ends in this many 0's in base 2 - Carl R. White, Jan 21 2008
These numbers are dead-end points when trying to apply the iterated process depicted in A071542 in reverse, i.e. these are positive integers i such that there does not exist k with A000120(i+k)=k. See also comments at A179016. - Antti Karttunen, Oct 26 2012
Conjecture: a(n)=b(n) defined as b(1)=2, for n>1, b(n+1)=b(n)+1 if n is already in the sequence, b(n+1)=b(n)+3 otherwise. If so, then see Cloitre comment in A080578. - Ralf Stephan, Dec 27 2013
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LINKS
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FORMULA
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Other identities. For all n >= 1:
(End)
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EXAMPLE
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Since A005187 begins 0 1 3 4 7 8 10 11 15 16 18 19 22 23 25 26 31... this sequence begins 2 5 6 9 12 13 14 17 20 21
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MATHEMATICA
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a[0] = 0; a[1] = 1; a[n_Integer] := a[Floor[n/2]] + n; b = {}; Do[ b = Append[b, a[n]], {n, 0, 105}]; c =Table[n, {n, 0, 200}]; Complement[c, b]
(* Second program: *)
t = Table[IntegerExponent[(2n)!, 2], {n, 0, 100}]; Complement[Range[t // Last], t] (* Jean-François Alcover, Nov 15 2016 *)
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PROG
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(Haskell)
a055938 n = a055938_list !! (n-1)
a055938_list = concat $
zipWith (\u v -> [u+1..v-1]) a005187_list $ tail a005187_list
(PARI) L=listcreate(); for(n=1, 1000, for(k=2*n-hammingweight(n)+1, 2*n+1-hammingweight(n+1), listput(L, k))); Vec(L) \\ Ralf Stephan, Dec 27 2013
(Scheme) ;; utilizing COMPLEMENT-macro from Antti Karttunen's IntSeq-library)
(Python)
def a053644(n): return 0 if n==0 else 2**(len(bin(n)[2:]) - 1)
def a043545(n):
x=bin(n)[2:]
return int(max(x)) - int(min(x))
def a079559(n): return 1 if n==0 else a043545(n + 1)*a079559(n + 1 - a053644(n + 1))
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CROSSREFS
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Cf. also A010061 (integers that are not a sum of distinct integers of the form 2^k+1).
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KEYWORD
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easy,nice,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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