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Search: id:A132669
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| A132669 |
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a(1)=1, a(n)=5*a(n-1) if the minimal natural number not encountered so far is greater than a(n-1), else a(n)=a(n-1)-1. |
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7
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| 1, 5, 4, 3, 2, 10, 9, 8, 7, 6, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 155, 154, 153, 152, 151, 150, 149, 148, 147, 146, 145, 144, 143
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OFFSET
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1,2
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COMMENT
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Also: a(1)=1, a(n)=maximal positive number <a(n-1) not encountered so far, if existing, else a(n)=5*a(n-1).
Also: a(1)=1, a(n)=a(n-1)-1, if a(n-1)-1>0 and has not been encountered so far, else a(n)=5*a(n-1).
A reordering of the natural numbers. The sequence is self-inverse, in that a(a(n))=n.
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FORMULA
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G.f.: g(x)=(x(1-2x)/(1-x)+5x^2*f'(x^(9/4))+(9/25)*(f'(x^(1/4))-5x-1))/(1-x) where f(x)=sum{k>=0, x^(5^k)} and f'(z)=derivative of f(x) at x=z.
a(n)=(14*5^(r/2)-6)/4-n, if both r and s are even, else a(n)=(34*5^((s-1)/2)-6)/4-n, where r=ceiling(2*log_5((4n+5)/9)) and s=ceiling(2*log_5((4n+5)/5))-1.
a(n)=(5^floor(1+(k+1)/2)+9*5^floor(k/2)-6)/4-n, where k=r, if r is odd, else k=s (with respect to r and s above; formally, k=((r+s)-(r-s)*(-1)^r)/2).
a(n)=A133629(m)+A133629(m+1)+1-n, where m:=max{ k | A133629(k)<n }.
a(A133629(n)+1)=A133629(n+1).
a(A133629(n))=A133629(n-1)+1 for n>0.
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CROSSREFS
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Cf. For formulas concerning a general parameter p (with respect to the recurrence rule ... a(n)=p*a(n-1) ...) see A132374.
Cf. For p=2 to p=10 see A132666-132674.
Cf. A133627.
Sequence in context: A081760 A094097 A145330 this_sequence A061836 A021188 A019762
Adjacent sequences: A132666 A132667 A132668 this_sequence A132670 A132671 A132672
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KEYWORD
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nonn
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AUTHOR
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Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 15 2007, Sep 23 2007
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