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A167450 Smallest sequence which lists the position of digits "8" in the sequence. 1

%I

%S 2,8,9,10,11,88,880,900,901,902,903,904,905,906,907,909,910,911,912,

%T 913,914,915,916,917,919,920,921,922,923,924,925,926,8000,9000,9001,

%U 9002,9003,9004,9005,9006,9007,9009,9010,9011,9012,9013,9014,9015,9016,9017

%N Smallest sequence which lists the position of digits "8" in the sequence.

%C The lexicographically earliest sequence such that a(1),a(2),a(3),... is the (increasing) list of the positions of digits "8" in the string obtained by concatenating all these terms, written in base 10.

%e We cannot have a(1)=1 (since then there's no "8" in the first place), but a(1)=2 is possible.

%e This implies that a(2) must start with a digit "8", so a(2)=8 is the smallest possible choice.

%e This allows us to go on with a(3)=9, a(4)=10, a(5)=11, but then must be follow 4 digits "8" (the 8th through 11th digit of the sequence), so a(6)=88 and a(7)=880 are the smallest possible choices.

%e Then the reasoning continues in analogy with A167452-A167457.

%o (PARI) concat([ [2,8,9,10,11,88,880], vector((88-11-1)\3,i,900-(i<=8)+i+(i>=18)), [8000], select(x->x%10-8 & x\10%10-8,vector((880-88)\4,i,9000-1+i)) ])

%Y Cf. A098645, A167519, A167520, A167451 - A167457.

%K base,nonn

%O 1,1

%A _M. F. Hasler_, Nov 19 2009

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Last modified March 30 12:10 EDT 2020. Contains 333125 sequences. (Running on oeis4.)