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Search: id:A109022
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| A109022 |
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Integers with mutual residues of 2 or more. |
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+0
9
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| 3, 5, 8, 14, 23, 38, 44, 53, 59, 62, 68, 74, 83, 122, 134, 143, 158, 164, 173, 179, 188, 194, 203, 218, 227, 242, 263, 278, 284, 293, 302, 314, 338, 362, 374, 383, 398, 404, 422, 428, 443, 452, 458, 467, 479, 482, 503, 509, 524, 539, 542, 548, 554, 563, 578
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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This is the special case k=2 of sequences with mutual k-residues. In general, a(1)=k+1 and a(n)=min{m | m>a(n-1), mod(m,a(i))>=k, i=1,...,n-1}. k=0 gives natural numbers A000027 and k=1 prime numbers A000040.
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LINKS
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S. Mustonen, On integer sequences with mutual k-residues
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EXAMPLE
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The fourth term is 14 since mod(9,3)=0, mod(10,3)=1, mod(11,5)=1,
mod(12,3)=0, mod(13,3)=1 but mod(14,3)=2, mod(14,5)=4, mod(14,8)=6.
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MAPLE
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res_seq:=proc(a::array(1, nonnegint), k, n::nonnegint) local i, j, m, f; a[1]:=k+1; for i from 2 to n do m:=a[i-1]+1; f:=1; while f=1 do j:=1; while j<i and irem(m, a[j])>=k do j:=j+1; od; if j=i then a[i]:=m; f:=0; else m:=m+1; fi; od; od; end; a:=array(1..57, []); res_seq(a, 2, 57); print(a);
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CROSSREFS
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Cf. A109328-A109335.
Sequence in context: A070948 A141739 A094007 this_sequence A023596 A086661 A078065
Adjacent sequences: A109019 A109020 A109021 this_sequence A109023 A109024 A109025
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KEYWORD
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nonn
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AUTHOR
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Seppo Mustonen (seppo.mustonen(AT)helsinki.fi), Aug 18 2005
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