A178404 Numbers such that the rounded up arithmetic mean of their digits equals their digital root.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 99, 100, 149, 158, 167, 176, 185, 194, 239, 248, 257, 266, 275, 284, 293, 329, 338, 347, 356, 365, 374, 383, 392, 419, 428, 437, 446, 455, 464, 473, 482, 491, 509, 518, 527, 536, 545, 554, 563, 572, 581, 590, 608, 617, 626, 635

Offset: 1

Author

Reinhard Zumkeller, May 27 2010

Keywords

• base
• easy
• nonn

Comments

A004427(a(n)) = A010888(a(n)); complement of A178405.

Examples

			From _Reinhard Zumkeller_, May 28 2010: (Start)
1093 --> 1+0+9+3=13 --> A010888(1093) = 1+3 = 4 and also
1093 --> 1+0+9+3=13 --> A004427(1093) = ceiling(13/4) = 4,
therefore 1093 is a term: a(100) = 1093. (End)
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A004427, A010888, A178405.

Programs

Maple

A178404 := proc(n) option remember: local k: if(n=1)then return 0: fi: k:=procname(n-1)+1: do if(ceil(add(d, d=convert(k,base,10))/length(k))-1 = (k-1) mod 9)then return k: fi: k:=k+1: od: end: seq(A178404(n),n=1..57); # Nathaniel Johnston, May 04 2011

Mathematica

amdrQ[n_]:=NestWhile[Total[IntegerDigits[#]]&,n,#>9&]==Ceiling[ Mean[ IntegerDigits[n]]]; Select[Range[0,1000],amdrQ] (* Harvey P. Dale, Oct 10 2013 *)