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A166747
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Numbers with n digits from the set {1,2,4}, requiring a non-decreasing sequence of digits and a digits sum of A008578(n).
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1
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1, 11, 111, 1112, 11122, 122222, 1222222, 12222224, 122222224, 1222222244, 12222224444, 122222224444, 1222222444444, 12222224444444, 122222224444444, 1222222244444444, 12222224444444444, 122222444444444444, 1222222444444444444, 12222244444444444444
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Or: a partitioning of p=A008578(n) into n parts, each part an element of {1,2,4}.
The representation is often not unique: p=11 could be represented by 111224 or 122222, p=13 by 1111144 or 1112224 or 1222222, p=17 by 11111444 or 11122244 or 12222224. a(n) selects the representation with the minimum number of 4's. [ R. J. Mathar, Oct 25 2009]
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MAPLE
| A008578 := proc(n) if n = 1 then 1; else ithprime(n-1) ; fi; end:
A166747 := proc(n) local p, n1, n2, n4, i ; p := A008578(n) ; for n4 from 0 to n do n2 := p-n-3*n4 ; n1 := n-n2-n4 ; if n2 >= 0 and n1 >= 0 then a := 0 ; for i from 1 to n1 do a := 10*a+1 ; od: for i from 1 to n2 do a := 10*a+2 ; od: for i from 1 to n4 do a := 10*a+4 ; od: return a ; end if: end do: end:
seq(A166747(n), n=1..20) ; # R. J. Mathar, Oct 25 2009
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CROSSREFS
| Cf. A134732.
Sequence in context: A078191 A097115 A134732 * A015456 A199764 A097177
Adjacent sequences: A166744 A166745 A166746 * A166748 A166749 A166750
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KEYWORD
| nonn,base
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), Oct 21 2009
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EXTENSIONS
| Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 25 2009
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