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A126712
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Height of steps in Recamán's sequence A064389.
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1
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0, 1, 1, 4, 4, 2, 2, 3, 3, 3, 3, 3, 3, 7, 5, 7, 7, 4, 4, 4, 4, 4, 4, 4, 4, 7, 5, 5, 5, 11, 11, 11, 11, 11, 11, 5, 11, 5, 5, 5, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 7, 11, 11, 11, 6, 6, 11, 9, 9, 6, 6, 11, 8, 8, 8, 6, 8, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7
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OFFSET
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1,4
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LINKS
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EXAMPLE
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The heights to reach 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24 in A064389 are b(1,2,3,...) = 0, 1, 2, 1, 2, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 4, 5 etc., as defined by b(n) = b(n-1) + sign(A064389(n) - A064389(n-1)).
Reshuffling sequence b while sorting A064489 into A078758 produces sequence a here, a(n) = b(A078758(n)).
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MAPLE
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A064389 := proc(nmax) local a, n, adiff, newa ; a := [1] ; for n from 2 to nmax do adiff := n ; while true do newa := op(-1, a)-adiff ; if newa >0 and not newa in a then a := [op(a), newa] ; break ; fi ; newa := op(-1, a)+adiff ; if newa >0 and not newa in a then a := [op(a), newa] ; break ; fi ; adiff := adiff+1 ; od ; od ; RETURN(a) ; end: A064389b := proc(a) local n, hei ; hei := [0] ; for n from 2 to nops(a) do hei := [op(hei), op(-1, hei)+sign(op(n, a)-op(n-1, a))] ; od ; RETURN(hei) ; end: inList := proc(list, n) local i ; for i from 1 to nops(list) do if op(i, list) = n then RETURN(i) ; fi ; od ; RETURN(-1) ; end: A078758 := proc(a064389) local a, n, i ; a := [] ; n :=1 ; while true do i := inList(a064389, n) ; if i < 0 then RETURN(a) ; else a := [op(a), i] ; n := n+1 ; fi ; od ; end: nmax := 1800 : a064389 := A064389(nmax) : a078758 := A078758(a064389) : b := A064389b(a064389) : for n from 1 to nops(a078758) do printf("%d, ", op(op(n, a078758), b)) ; od;
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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