A341767 -id:A341767 - cp's OEIS frontend

A348179 Replace each decimal digit d of n with the digit that is d steps to the right of d. Interpret the digits of n as a cycle: one step to the right from the last digit is considered to be the first.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 11, 22, 31, 44, 51, 66, 71, 88, 91, 20, 22, 22, 22, 24, 22, 26, 22, 28, 22, 0, 13, 22, 33, 44, 53, 66, 73, 88, 93, 40, 44, 42, 44, 44, 44, 46, 44, 48, 44, 0, 15, 22, 35, 44, 55, 66, 75, 88, 95, 60, 66, 62, 66, 64, 66, 66, 66, 68, 66, 0, 17, 22, 37, 44, 57, 66, 77, 88, 97, 80, 88, 82, 88, 84, 88, 86, 88, 88, 88, 0, 19, 22, 39, 44, 59, 66, 79, 88, 99, 0, 1

Offset: 0

Sebastian Karlsson, Oct 05 2021

First differs from A349422 at a(101). - Sebastian Karlsson, Dec 31 2021

			a(102345) = 004124 = 4124. For example, 4 gets replaced by 2 because moving 4 steps to the right gives: 4 -> 5 -> 1 -> 0 -> 2. Note that from 5 we went to the first digit of the number.

Sebastian Karlsson, Table of n, a(n) for n = 0..10000

Cf. A336668 (fixed points), A349422 (to the left), A349423 (index of first appearance of n).

Cf. A106649, A139337, A322131, A339023, A341767, A341953, A346576, A347323.

import Data.Char (digitToInt)
a n = let s = show n; l = length s in
  read [s !! (mod (i + digitToInt (s !! i)) l) | i <- [0..l-1]] :: Integer

Table[FromDigits@Table[v[[If[(p=Mod[k+v[[k]],t])==0,t,p]]],{k,t=Length[v=IntegerDigits[n]]}],{n,0,67}] (* Giorgos Kalogeropoulos, Oct 08 2021 *)

f(k, d) = d[(k+d[k]-1)%#d + 1];
a(n) = my(d=digits(n), dd=vector(#d, k, f(k, d))); fromdigits(dd); \\ Michel Marcus, Oct 07 2021

def a(n):
    s, l = str(n), len(str(n))
    return int("".join(s[(i + int(s[i])) % l] for i in range(l)))

a(68)-a(101) from Sebastian Karlsson, Dec 31 2021

A341953 Replace each digit d in the decimal representation of n with the digital root of d^n.

Original entry on oeis.org

1, 4, 9, 4, 2, 9, 7, 1, 9, 10, 11, 11, 19, 17, 18, 19, 14, 11, 19, 40, 81, 77, 59, 11, 25, 49, 81, 71, 59, 90, 91, 94, 99, 94, 92, 99, 97, 91, 99, 40, 71, 11, 49, 77, 18, 49, 74, 11, 49, 70, 81, 47, 29, 11, 55, 79, 81, 41, 29, 90, 91, 94, 99, 94, 92, 99, 97

Offset: 1

Sebastian Karlsson, Feb 24 2021

The digits 0, 1, 3, 6 and 9 will always be replaced by the same digits: 0 -> 0, 1 -> 1, 3 -> 9, 6 -> 9 and 9 -> 9.

			a(14) = 17, since 1^14 = 1 and 4^14 = 268435456. 2 + 6 + 8 + 4 + 3 + 5 + 4 + 5 + 6 = 43 and 4 + 3 = 7. Thus, the digital root of 268435456 is 7. This means that for 14, "1" gets replaced by "1" and "4" gets replaced by "7".

Robert Israel, Table of n, a(n) for n = 1..10000
Sebastian Karlsson, Generalized and plotted in arbitrary bases

Cf. A010888, A106649, A139337, A322131, A339023, A341767.

digroot[n_] := If[n == 0, 0, Mod[n - 1, 9] + 1]; a[n_] := FromDigits[digroot /@ (IntegerDigits[n]^n)]; Array[a, 100] (* Amiram Eldar, Feb 24 2021 *)

r(n) = if(n, (n-1)%9+1) \\ A010888
a(n) = fromdigits(apply(x->r(x^n), digits(n))); \\ Michel Marcus, Mar 21 2021

def D(d, n):
    return 0 if d == 0 else (pow(d, n, 9)-1)%9 + 1
def a(n):
    return int(''.join(str(D(int(d), n)) for d in str(n)))

cp's OEIS Frontend

A348179 Replace each decimal digit d of n with the digit that is d steps to the right of d. Interpret the digits of n as a cycle: one step to the right from the last digit is considered to be the first.

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