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A076125
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Define r(k) as follows: r(1)=n, r(k+1) = r(k) +(-1)^k*sign(r(k)-k)*k; then abs(r(k)) = n for at least one k>1 (there could be 2 values for k>1). Sequence gives the smallest value of k>1 such that abs(r(k)) = n.
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0
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2, 4, 9, 8, 8, 25, 12, 12, 29, 16, 16, 37, 20, 20, 61, 24, 24, 57, 28, 28, 65, 32, 32, 129, 36, 36, 85, 40, 40, 93, 44, 44, 129, 48, 48, 113, 52, 52, 121, 56, 56, 165, 60, 60, 141, 64, 64, 149, 68, 68, 265, 72, 72, 169, 76, 76, 177, 80, 80, 233, 84, 84, 197, 88, 88, 205
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| If n=3k+1 or 3k+2, abs(r(x))=n for x=4k+4 and x=8k+1 (first solution only is in the sequence). This was inspired by the Recaman sequence (A005132).
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FORMULA
| For k>=1, a(3k+1)=a(3k+2)=4k+4; for m>=2, k>=1, a(3^m*k)=3^(m-2)*28*k+1. For a(3^m*k+a) it is more complicate to give a general formula, as examples: a(9k+3)=28k+9; a(9k+6)=36k+25; a(27k+3)=84k+9; a(27k+6)=104k+25; a(27k+9)=84k+29; a(27k+12)=84k+37; a(27k+24)=136k+129. sum(k=1, n, a(k)) is asymptotic to n^2.
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EXAMPLE
| If r(1)=5: r(8)=5, hence a(5)=8
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CROSSREFS
| Cf. A005132.
Sequence in context: A055858 A141389 A133757 * A011033 A179219 A033149
Adjacent sequences: A076122 A076123 A076124 * A076126 A076127 A076128
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 31 2002
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