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

1,4

Links

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

Formula

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

Example

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

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 *)

Prog

(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
(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

Crossrefs

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

Cf. A095221.

Sequence in context: A128200 A258168 A061988 * A135800 A178152 A006984

Adjacent sequences: A094148 A094149 A094150 * A094152 A094153 A094154

Keyword

nonn,base,easy

Author

Amarnath Murthy, Apr 29 2004

Extensions

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

Status

approved