A091023 a(1)=1; for n >= 2, set a(n)=m, where n is the smallest unassigned index with exactly m-1 unassigned indices still remaining between m and m-1.
1, 2, 13, 3, 6, 26, 4, 11, 205, 9, 5, 24, 7, 51, 22, 102, 20, 49, 18, 8, 410, 10, 16, 12, 47, 14, 100, 45, 203, 43, 98, 41, 3277, 39, 96, 37, 201, 35, 94, 15, 33, 17, 408, 19, 31, 21, 92, 23, 29, 25, 199, 27, 90, 819, 88, 197, 86, 406, 84, 195, 82, 1638, 80, 193, 78, 404
Offset: 1
Examples
After 1 has been assigned to a(1), the first unassigned term that is one term away from 1 is a(2), so a(2)=2; the first unassigned term that is two terms away from 2 is a(4), so a(4)=3; the first unassigned term that is 3 terms away from 3 is a(7), so a(7)=4; the first unassigned term that is 4 terms away from 4 is a(11), so a(11)=5; at this point we have 1,2,*,3,*,*,4,*,*,*,5,..., where * indicates a term to which a value has not yet been assigned. The next value to assign is 6 which must be assigned to the first term of the sequence that is 5 terms away from a(11)=5; since a(5) has not yet been assigned a value and since at this point 5 terms with unassigned values lie between a(5) and a(11), we must assign 6 to a(5), i.e., a(5)=6.
Links
- R. J. Mathar, Apr 28 2007, Table of n, a(n) for n = 1..78
- Hans Havermann, Illustration of first 1600 terms (with some gaps)
Programs
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Maple
nmax := 20000 : a := [seq(0,i=1..nmax)] : a := subsop(1=1,a) : a := subsop(2=2,a) : prevn := 2 : n := 3: while true do us := n ; atst := prevn-1 ; tstdown := false ; while us > 0 and atst>0 do if op(atst,a) =0 then us := us-1 ; if us = 1 then tstdown := true ; a := subsop(atst=n,a) ; prevn := atst ; break ; fi ; fi ; atst := atst -1 ; od ; if tstdown = false then us := n ; atst := prevn+1 ; while us > 0 do if op(atst,a) =0 then us := us-1 ; if us = 1 then a := subsop(atst=n,a) ; prevn := atst ; break ; fi ; fi ; atst := atst +1 ; od ; fi ; for i from 1 to 150 do printf("%d, ",op(i,a)) ; od ; print() ; n := n+1 ; od : # R. J. Mathar, Apr 28 2007
Extensions
More terms from R. J. Mathar, Apr 28 2007
Comments