A094151 Remainder when concatenation 1,2,3,...up to (n-1) is divided by n.

0, 1, 0, 3, 4, 3, 4, 7, 0, 9, 4, 3, 12, 9, 9, 7, 1, 9, 7, 19, 12, 15, 18, 15, 24, 9, 0, 11, 27, 9, 7, 7, 15, 9, 9, 27, 29, 21, 21, 39, 22, 33, 5, 15, 9, 39, 45, 39, 39, 49, 27, 51, 33, 27, 4, 23, 15, 49, 49, 39, 32, 13, 54, 7, 9, 15, 41, 59, 0, 39, 47, 63, 41, 17, 24, 23, 37, 21, 75, 39

Offset: 1

Author

Amarnath Murthy, Apr 29 2004

Keywords

• nonn
• base
• easy

Examples

			a(5) = 15 hence a(6) = least integer multiple of 15/6 = 5.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007908, A110740 (indices of 0's).

Cf. A095221.

Programs

Mathematica

Table[st = ""; For[i = 0, i <= n - 1, i++, st = st <> ToString[i]]; Mod[ ToExpression[st], n], {n, 1, 100}] (* Sam Handler (sam_5_5_5_0(AT)yahoo.com), Nov 12 2004 *)
Table[Mod[FromDigits[Flatten[IntegerDigits/@Range[n-1]]],n],{n,100}] (* Harvey P. Dale, May 21 2024 *)

PARI

a(n)=if(n<=9, return(1719%n)); my(m=Mod(123456789,n)); for(d=2,#Str(n-1), my(D=10^d); for(k=D/10,min(D,n)-1, m=D*m+k)); lift(m) \\ Charles R Greathouse IV, Nov 21 2022

Python

from itertools import count, islice
def agen():
    s = "0"
    for n in count(1): yield int(s)%n; s += str(n)
print(list(islice(agen(), 80))) # Michael S. Branicky, Nov 21 2022

Formula

a(n) = A007908(n-1) mod n for n>1. - Michel Marcus, Nov 21 2022

Extensions

More terms from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Nov 12 2004