A095221 -id:A095221 - cp's OEIS frontend

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

Amarnath Murthy, Apr 29 2004

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

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

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

Cf. A095221.

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 *)

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

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

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

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

A281066 Concatenation R(n)R(n-1)R(n-2)...R(2)R(1) read mod n, where R(x) is the digit-reversal of x (with leading zeros not omitted).

Original entry on oeis.org

0, 1, 0, 1, 1, 3, 3, 1, 0, 1, 4, 9, 5, 7, 6, 1, 6, 9, 17, 1, 15, 15, 19, 9, 21, 1, 18, 13, 28, 21, 26, 17, 15, 3, 16, 9, 30, 3, 15, 1, 1, 33, 10, 37, 36, 43, 22, 33, 19, 21, 48, 45, 2, 45, 26, 49, 27, 33, 33, 21, 48, 25, 36, 49, 36, 15, 22, 5, 27, 11, 42, 9, 2, 73, 21, 17, 59, 57, 5, 1

Offset: 1

Robert G. Wilson v, Jan 14 2017

			a(13) = 31211101987654321 (mod 13) = 5.

Indranil Ghosh, Table of n, a(n) for n = 1..20008

Cf. A004086, A061963, A095221, A114795, A138793.

f[n_] := Mod[ FromDigits@ Fold[ Join[ Reverse@ IntegerDigits@#2, #1] &, {}, Range@ n], n]; Array[f, 80]

a(n) = my(s = ""); forstep (k=n,1,-1, sk = digits(k); forstep (j=#sk, 1, -1, s = concat(s, sk[j]))); eval(s) % n; \\ Michel Marcus, Jan 28 2017

def A281066(n):
    s=""
    for i in range(n, 0, -1):
        s+=str(i)[::-1]
    return int(s)%n # Indranil Ghosh, Jan 28 2017

a(n) = A138793(n) (mod n).

A281190 Concatenation of the reversed digits of numbers from 1 to n, mod n.

Original entry on oeis.org

0, 0, 0, 2, 0, 0, 5, 6, 0, 1, 6, 9, 3, 1, 6, 9, 5, 9, 1, 2, 18, 6, 12, 18, 2, 6, 18, 26, 7, 3, 20, 27, 6, 3, 28, 27, 7, 19, 12, 24, 4, 24, 12, 28, 9, 8, 42, 12, 22, 5, 3, 45, 41, 45, 50, 45, 45, 23, 16, 6, 6, 54, 27, 30, 61, 6, 37, 30, 21, 67, 47, 63, 52, 67, 57, 19, 28, 15, 58, 28, 72, 22, 56, 24, 83, 34, 3, 72, 72, 9, 85, 69, 57

Offset: 1

Robert G. Wilson v, Jan 16 2017

Note that leading zeros are not omitted when numbers are reversed. - N. J. A. Sloane, Jan 23 2017

			a(13) = A138957(13) mod 13 == 12345678901112131 mod 13 == 3.

Indranil Ghosh, Table of n, a(n) for n = 1..20008

Cf. A029503, A095221, A114795, A138957, A281066.

f[n_] := Mod[ Fold[#1*10^IntegerLength@#2 + FromDigits@ Reverse@ IntegerDigits@#2 &, 0, Range@ n], n]; Array[f, 105]

a(n) = my(s = ""); for (k=1, n, sk = digits(k); forstep (j=#sk, 1, -1, s = concat(s, sk[j]))); eval(s) % n; \\ Michel Marcus, Jan 28 2017

def A281190(n):
    s=""
    for i in range(1,n+1):
        s+=str(i)[::-1]
    return int(s)%n # Indranil Ghosh, Jan 28 2017

a(n) = A138957(n) mod n.

cp's OEIS Frontend

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

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

Formula

Extensions

A281066 Concatenation R(n)R(n-1)R(n-2)...R(2)R(1) read mod n, where R(x) is the digit-reversal of x (with leading zeros not omitted).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

Formula

A281190 Concatenation of the reversed digits of numbers from 1 to n, mod n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

Formula