A075329 Pair up the natural numbers as (r, s) (say) so that all natural numbers are obtained only once as r, s, s+r or s-r: (1, 3), (5, 11), (7, 15), (9, 19), (12, 25), (14, 31), (18, 38), ... Sequence gives first member of each pair.
1, 5, 7, 9, 12, 14, 18, 21, 24, 27, 29, 33, 35, 39, 41, 43, 47, 49, 51, 54, 58, 60, 63, 66, 69, 72, 75, 77, 78, 82, 86, 88, 92, 94, 96, 99, 103, 105, 110, 112, 114, 116, 120, 123, 126, 129, 130, 135, 137, 140, 143, 146, 148, 152, 154, 158, 160, 164, 166, 169, 171, 172
Offset: 1
Keywords
Programs
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Maple
A075329 := proc(nmax) local r,s,n,stst,rtst ; r := [1] : s := [] : n := {1} : while nops(r) < 100 do stst := 1 ; while stst in n or stst-op(-1,r) in n or stst+op(-1,r) in n do stst := stst +1 ; od ; s := [op(s),stst] ; n := n union {stst, stst-op(-1,r), stst+op(-1,r)} ; rtst := 1 ; while rtst in n do rtst := rtst +1 ; od ; r := [op(r),rtst] ; n := n union {rtst} ; od : RETURN(r) ; end: A075329(100) ; # R. J. Mathar, Feb 03 2007
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Mathematica
A075329[nmax_] := Module[{r = {1}, s = {}, n = {1}, stst, rtst}, While[Length[r] < nmax, stst = 1; While[MemberQ[n, stst] || MemberQ[n, stst - Last[r]] || MemberQ[n, stst + Last[r]], stst++]; s = Append[s, stst]; n = n ~Union~ {stst, stst - Last[r], stst + Last[r]}; rtst = 1; While[MemberQ[n, rtst], rtst++]; r = Append[r, rtst]; n = n ~Union~ {rtst}]; Return[r]]; A075329[100] (* Jean-François Alcover, Jun 06 2024, after R. J. Mathar *)
Extensions
More terms from R. J. Mathar, Feb 03 2007