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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.
4
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
1,2
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
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Sep 18 2002
EXTENSIONS
More terms from R. J. Mathar, Feb 03 2007
STATUS
approved