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1, 2, 4, 5, 8, 9, 11, 12, 16, 17, 19, 20, 23, 24, 26, 27, 32, 33, 35, 36, 39, 40, 42, 43, 47, 48, 50, 51, 54, 55, 57, 58, 64, 65, 67, 68, 71, 72, 74, 75, 79, 80, 82, 83, 86, 87, 89, 90, 95, 96, 98, 99, 102, 103, 105, 106, 110, 111, 113, 114, 117, 118, 120, 121, 128, 129
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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p(n) sequence for k=2, s=0. p(n) = min(j: A046699(j) = n). - Frank Ruskey and Chris Deugau (deugaucj(AT)uvic.ca)
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LINKS
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FORMULA
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Recurrence: a(2n) = 2a(n) + A000120(n) - 1, a(2n+1) = a(2n) + 1.
G.f.: (1 / 1-z) * (z + z * sum(z^(2^i) * (s + (1 / (1 - z^(2^k)))),i=0..infinity)). - Frank Ruskey and Chris Deugau (deugaucj(AT)uvic.ca)
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MATHEMATICA
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Table[IntegerExponent[(2 n)!, 2] + 1, {n, 0, 65}] (* or *)
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PROG
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(PARI) a(n)=1+sum(k=1, n, valuation(k, 2)+1)
(PARI) a(n)=if(n==0, 1, if((n%2)==0, 2*a(n/2)+subst(Pol(binary(n)), x, 1)-1, a(n-1)+1))
(Python 3.10+)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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