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A156068
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The slowest increasing sequence such that there is no common digit between any two integers from {a(n), a(n-1), a(n-2), c=a(n)+a(n-1)+a(n-2)}.
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0
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1, 2, 3, 4, 5, 7, 8, 9, 10, 25, 33, 40, 55, 73, 81, 90, 262, 433, 880, 959, 2272, 3380, 5459, 7272
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OFFSET
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1,2
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COMMENTS
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For this particular case a(1..2)=1, 2 the sequence is complete with the last term a(24)=7272.
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LINKS
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EXAMPLE
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{a(n-2), a(n-1),a(n),c=a(n)+a(n-1)+a(n-2)}
{1,2,3,6}
{2,3,4,9}
{3,4,5,12}
{4,5,7,16}
{5,7,8,20}
{7,8,9,24}
{8,9,10,27}
{9,10,25,44}
{10,25,33,68}
{25,33,40,98}
{33,40,55,128}
{40,55,73,168}
{55,73,81,209}
{73,81,90,244}
{81,90,262,433}
{90,262,433,785}
{262,433,880,1575}
{433,880,959,2272}
{880,959,2272,4111}
{959,2272,3380,6611}
{2272,3380,5459,11111}
{3380,5459,7272,16111}.
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MATHEMATICA
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ss={1, 2}; a=1; b=2; ia=IntegerDigits[a]; ib=IntegerDigits[b]; Do[ic=IntegerDigits[c]; isu=IntegerDigits[su=a+b+c]; If[Intersection[ic, ia]==Intersection[ic, ib]==Intersection[ic, isu]==Intersection[ia, isu]==Intersection[ib, isu]=={}, Print[{a, b, c, su}]; AppendTo[ss, c]; a=b; b=c; ia=ib; ib=ic], {c, 3, 100000}]; ss
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CROSSREFS
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KEYWORD
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base,fini,full,nonn
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AUTHOR
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STATUS
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approved
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