The lexicographically smallest 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.
_M. F. Hasler (www.univ-ag.fr/~mhasler), _, Nov 19 2009
We cannot have a(1)=1 (since then there's no "8" in the 1st first place), but a(1)=2 is possible.
base,nonn,new
M. F. Hasler (MHasler(AT)www.univ-ag.fr/~mhasler), Nov 19 2009
Smallest sequence which lists the position of digits "8" in the sequence.
2, 8, 9, 10, 11, 88, 880, 900, 901, 902, 903, 904, 905, 906, 907, 909, 910, 911, 912, 913, 914, 915, 916, 917, 919, 920, 921, 922, 923, 924, 925, 926, 8000, 9000, 9001, 9002, 9003, 9004, 9005, 9006, 9007, 9009, 9010, 9011, 9012, 9013, 9014, 9015, 9016, 9017
1,1
The lexicographically smallest 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.
We cannot have a(1)=1 (since then there's no "8" in the 1st place), but a(1)=2 is possible.
This implies that a(2) must start with a digit "8", so a(2)=8 is the smallest possible choice.
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.
Then the reasoning continues in analogy with A167452-A167457.
(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)) ])
base,nonn
M. F. Hasler (MHasler(AT)univ-ag.fr), Nov 19 2009
approved