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Search: id:A095115
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| A095115 |
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a(1)=1. Given a(1),...,a(n-1), let S = {a(1), ..., a(n-1), |a(2)-a(1)|, ..., |a(n-1)-a(n-2)|}. Let d be the smallest positive integer not in S. Then a(n) is the smallest one of a(n-1)-d and a(n-1)+d which is a positive integer not in S union {d}. |
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+0
1
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| 1, 3, 7, 12, 18, 10, 19, 30, 17, 31, 16, 36, 57, 35, 58, 34, 59, 33, 60, 32, 61, 98, 136, 97, 137, 96, 54
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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EXAMPLE
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For n=5, S={1,3,7,12, 2,4,5} so d=6. a(4)-d=6 is in S union {6}, so we have a(5)=a(4)+d=18.
a(28) does not exist: d=43, but both a(28)-43=11 and a(28)+43=97 are in S union {43}.
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MATHEMATICA
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mex1[s_]:=Module[{n}, For[n=1, MemberQ[s, n], n++, Null]; n]; a[1]=1; a[n_]:=a[n]=Module[{as, d}, as=a/@Range[n-1]; as=Union[as, Abs[Drop[as, 1]-Drop[as, -1]]]; AppendTo[as, d=mex1[as]]; If[a[n-1]-d>0&&!MemberQ[as, a[n-1]-d], a[n-1]-d, If[ !MemberQ[as, a[n-1]+d], a[n-1]+d], False]]
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CROSSREFS
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Adjacent sequences: A095112 A095113 A095114 this_sequence A095116 A095117 A095118
Sequence in context: A084582 A072098 A140778 this_sequence A141214 A027379 A055998
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KEYWORD
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nonn,fini,full
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AUTHOR
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Dean Hickerson (dean.hickerson(AT)yahoo.com), following a suggestion of Leroy Quet May 28 2004
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