A167455 Smallest sequence which lists the position of digits "5" in the sequence.
2, 5, 6, 7, 55, 56, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 81, 82, 83, 84, 550, 605, 5555, 6555, 55555, 56555, 555555, 600000, 600001, 600002, 600003, 600004, 600006, 600007, 600008, 600009, 600010, 600011, 600012, 600013
Offset: 1
Examples
We cannot have a(1)=1 (since then there's no "5" in the first place), but a(1)=2 is possible. Then a(2) must start with a digit "5", so a(2)=5 is the smallest possible choice. This allows us to go on with a(3)=6, a(4)=6, but then must be follow 3 digits "5" (the 5th, 6th and 7th digit of the sequence), so a(5)=55 and a(6)=56 are the smallest possible choice. The reasoning continues in analogy with A167452-A167454.
Programs
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PARI
concat([ [2,5,6,7,55,56], vector((55-8)\2,i,60-(i<=5)+i+(i>=15)), [550, 605, 5555, 6555, 55 555, 56 555, 555 555], select(x->x%10-5 & x\10%10-5,vector((550-84)\6+10,i,600 000+i-1)) ])
Comments