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

1,2

Links

Table of n, a(n) for n=1..62.

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

Cf. A075330, A075331, A075332.

Sequence in context: A374786 A184102 A285915 * A177031 A336008 A159018

Adjacent sequences: A075326 A075327 A075328 * A075330 A075331 A075332

Keyword

nonn

Author

Amarnath Murthy, Sep 18 2002

Extensions

More terms from R. J. Mathar, Feb 03 2007

Status

approved