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

Author

R. J. Mathar, Feb 12 2007

Keywords

• easy
• nonn

Examples

			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)).
		

Crossrefs

Cf. A064389, A078758.

Programs

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;