A126712 Height of steps in Recamán's sequence A064389.

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

Offset

1,4

Links

Table of n, a(n) for n=1..96.

Example

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)).

Maple

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;

Crossrefs

Cf. A064389, A078758.

Sequence in context: A366470 A192977 A038800 * A162232 A029676 A105190

Adjacent sequences: A126709 A126710 A126711 * A126713 A126714 A126715

Keyword

easy,nonn

Author

R. J. Mathar, Feb 12 2007

Status

approved