A166747 Numbers with n digits from the set {1,2,4}, requiring a nondecreasing sequence of digits and a digits sum of A008578(n).

1, 11, 111, 1112, 11122, 122222, 1222222, 12222224, 122222224, 1222222244, 12222224444, 122222224444, 1222222444444, 12222224444444, 122222224444444, 1222222244444444, 12222224444444444, 122222444444444444, 1222222444444444444, 12222244444444444444

Offset: 1

Author

Paul Curtz, Oct 21 2009

Keywords

• nonn
• base

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

Crossrefs

Cf. A134732.

Programs

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

Extensions

Edited by R. J. Mathar, Oct 25 2009