A156068 - OEIS

%I #3 Nov 16 2017 15:52:24

%S 1,2,3,4,5,7,8,9,10,25,33,40,55,73,81,90,262,433,880,959,2272,3380,

%T 5459,7272

%N 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)}.

%C For this particular case a(1..2)=1, 2 the sequence is complete with the last term a(24)=7272.

%e {a(n-2), a(n-1),a(n),c=a(n)+a(n-1)+a(n-2)}

%e {1,2,3,6}

%e {2,3,4,9}

%e {3,4,5,12}

%e {4,5,7,16}

%e {5,7,8,20}

%e {7,8,9,24}

%e {8,9,10,27}

%e {9,10,25,44}

%e {10,25,33,68}

%e {25,33,40,98}

%e {33,40,55,128}

%e {40,55,73,168}

%e {55,73,81,209}

%e {73,81,90,244}

%e {81,90,262,433}

%e {90,262,433,785}

%e {262,433,880,1575}

%e {433,880,959,2272}

%e {880,959,2272,4111}

%e {959,2272,3380,6611}

%e {2272,3380,5459,11111}

%e {3380,5459,7272,16111}.

%t 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

%Y Cf. A166461.

%K base,fini,full,nonn

%O 1,2

%A _Zak Seidov_, Oct 23 2009