A114795 -id:A114795 - cp's OEIS frontend

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).

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).

A280987 {Concatenation n, n-1, n-2, ...3,2,1} mod sigma(n).

Original entry on oeis.org

0, 0, 1, 2, 3, 9, 1, 6, 4, 1, 9, 21, 1, 9, 9, 16, 9, 24, 1, 33, 17, 1, 9, 21, 0, 9, 1, 41, 21, 33, 17, 6, 33, 19, 33, 25, 25, 21, 1, 1, 33, 81, 17, 21, 45, 1, 33, 85, 49, 69, 57, 77, 27, 81, 1, 81, 1, 1, 21, 57, 59, 81, 33, 60, 21, 33, 45, 51, 81, 1, 9, 66, 41, 9, 97, 1, 81, 81, 1, 57, 117, 73, 33, 145

Offset: 1

Indranil Ghosh, Jan 12 2017

			For n = 11, A000422(n) mod sigma(n) = 1110987654321 mod 12 = 9. S0 a(11) = 9.

Indranil Ghosh, Table of n, a(n) for n = 1..10000

Cf. A000203, A000422, A114795.

Table[Mod[FromDigits[Flatten[IntegerDigits/@Range[n,1,-1]]],DivisorSigma[ 1,n]],{n,90}] (* Harvey P. Dale, Jul 01 2020 *)

def sigma(n):
    s=0
    for i in range(1,n+1):
        if n%i==0:
            s+=i
    return s
def C(n):
    s=""
    for i in range(n,0,-1):
        s+=str(i)
    return int(s)
for i in range(1,101):
    print(i, C(i)%sigma(i))

from sympy import divisor_sigma
def A280987(n): return int(''.join(map(str, range(n, 0, -1)))) % divisor_sigma(n) # David Radcliffe, Aug 08 2025

a(n) = A000422(n) mod A000203(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

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).

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A280987 {Concatenation n, n-1, n-2, ...3,2,1} mod sigma(n).

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

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