A087144 Numbers with sum of digits not divisible by digital root.

29, 38, 47, 49, 56, 58, 59, 65, 67, 68, 69, 74, 76, 77, 78, 79, 83, 85, 86, 87, 88, 89, 92, 94, 95, 96, 97, 98, 119, 128, 137, 139, 146, 148, 149, 155, 157, 158, 159, 164, 166, 167, 168, 169, 173, 175, 176, 177, 178, 179, 182, 184, 185, 186, 187, 188, 191, 193, 194, 195, 196, 197, 209

Offset: 1

Author

Reinhard Zumkeller, Aug 18 2003

Keywords

• nonn
• base
• easy

Comments

A007953(a(n)) mod A010888(a(n)) > 0.

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Crossrefs

Complement of A087143.

A357772 is a subsequence.

Programs

Maple

A087144 := proc(n) option remember: local k: if(n=1)then return 29: fi: k:=procname(n-1)+1: do if(add(d, d=convert(k,base,10)) mod (((k-1) mod 9) + 1) > 0)then return k: fi: k:=k+1: od: end: seq(A087144(n),n=1..70); # Nathaniel Johnston, May 04 2011

Mathematica

ndQ[n_]:=Module[{tidn=Total[IntegerDigits[n]],dr},dr= NestWhile[Total[ IntegerDigits[#]]&,tidn,#>9&]; !Divisible[tidn,dr]]; Select[Range[200],ndQ] (* Harvey P. Dale, Apr 22 2011 *)

PARI

is(n)=sumdigits(n)%((n-1)%9+1) != 0 \\ Charles R Greathouse IV, Oct 13 2022

Formula

a(n) ~ n. - Charles R Greathouse IV, Oct 13 2022