A156068 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)}.

1, 2, 3, 4, 5, 7, 8, 9, 10, 25, 33, 40, 55, 73, 81, 90, 262, 433, 880, 959, 2272, 3380, 5459, 7272

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..24.

Example

{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}.

Mathematica

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

Crossrefs

Cf. A166461.

Sequence in context: A374759 A330220 A039169 * A039263 A344881 A039203

Adjacent sequences: A156065 A156066 A156067 * A156069 A156070 A156071

Keyword

base,fini,full,nonn

Author

Zak Seidov, Oct 23 2009

Status

approved