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A167454
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Smallest sequence which lists the position of digits "4" in the sequence.
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1
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2, 4, 5, 44, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 400, 500, 4444, 5444, 44444, 45444, 444000, 500000, 500001, 500002, 500003, 500005, 500006, 500007, 500008, 500009, 500010, 500011, 500012, 500013, 500015, 500016
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OFFSET
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1,1
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COMMENTS
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The lexicographically smallest sequence such that a(1),a(2),a(3),... is the (increasing) list of the positions of digits "4" in the string obtained by concatenating all these terms, written in base 10.
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LINKS
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Table of n, a(n) for n=1..45.
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EXAMPLE
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We cannot have a(1)=1 (since then there's no "4" in the first place), but a(1)=2 is possible.
Then a(2)=4 is the smallest possible choice.
This allows us to take a(3)=5, but this must be followed by two digits "4" (the 4th and 5th of the sequence), thus a(4)=44. Terms a(5) through a(5+(44-6)/2) are now to be filled with 50,51,..., omitting terms with a digit "4".
The last term of this series is 70, which must be followed by 400 (whose first digit is the 44-th digit of the sequence), 500, and then 4444 (digits 50-53), 5444 (digits 54-57), 44444 (digits 58-62), 45444 (digits 63-67), 444000 (digits 68-73). This "predicts" that a(3) starts with a digit "3", so a(3)=30 is the smallest possible choice.
The next digit "3" must not appear until the 30th digit of the sequence, so we fill in terms 40,41,42,44,45... (omitting 43 which has a digit "3").
Now it happens that the term 53 would correspond to digits # 29 and 30=a(3) of the sequence, so we can simply continue with this and 4 more terms, up to 57.
The next term must have it's second digit (digit # 40=a(4) of the sequence) equal to 3, so 63 is the smallest choice.
The terms a(5)=41, a(6)=42 leave 330 as the smallest possible choice for the next term.
The terms 44,45,46 and 47,48,49,50 and 51,52,53,54,55 lead to the subsequent terms 333, 3333, 33333.
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PROG
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(PARI) concat([[2, 4, 5, 44], vector((44-6)/2, i, 50-(i<=4)+i+(i>=14)), [400, 500, 4444, 5444, 44 444, 45 444, 444000], select(x->x%10-4 & x\10%10-4, vector((400-70)\6+10, i, 500 000+i-1)) ])
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CROSSREFS
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Cf. A098645, A167519, A167520, A167452, A167453.
Sequence in context: A126666 A154775 A210418 * A056683 A105288 A066684
Adjacent sequences: A167451 A167452 A167453 * A167455 A167456 A167457
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KEYWORD
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base,nonn
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AUTHOR
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M. F. Hasler, Nov 19 2009
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STATUS
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approved
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