A346576 -id:A346576 - cp's OEIS frontend

A347323 Replace each nonzero digit d of n by (n mod d).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 4, 3, 2, 1, 0, 10, 0, 12, 0, 10, 2, 16, 4, 12, 0, 10, 20, 0, 12, 20, 0, 12, 26, 3, 0, 10, 20, 31, 0, 10, 24, 35, 0, 14, 0, 10, 20, 32, 42, 0, 12, 21, 32, 45, 0, 10, 20, 30, 40, 50, 0, 14, 24, 36, 0, 10, 20, 31, 42, 50

Offset: 0

N. J. A. Sloane, Sep 13 2021

The zero digits are preserved, but after the other digits have been changed leading zeros are of course omitted.

			a(23) = 12, since 23 mod 2 is 1, 23 mod 3 is 2.
a(24) = 0, since both 24 mod 2 and 24 mod 4 are 0.
a(25) = 10 since 25 mod 2 is 1, 25 mod 5 is 0.

Michel Marcus, Table of n, a(n) for n = 0..10000

Suggested by A346576.

a[0] = 0; a[n_] := FromDigits[Mod[n, IntegerDigits[n]/.{0->n}]]; Array[a, 100, 0] (* Amiram Eldar, Sep 13 2021 *)

a(n) = my(d=digits(n)); fromdigits(vector(#d, k, if (d[k], n % d[k], 0))); \\ Michel Marcus, Sep 13 2021

def A347323(n): return int(''.join('0' if d == '0' else str(n % int(d)) for d in str(n))) # Chai Wah Wu, Sep 13 2021

More terms from Stefano Spezia, Sep 13 2021

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.

Original entry on oeis.org

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

A349422 Replace each decimal digit d of n with the digit that is d steps to the left of d. Interpret the digits of n as a cycle: one step to the left from the first digit is considered to be the last.

Original entry on oeis.org

Offset: 0

Sebastian Karlsson, Nov 17 2021

First differs from A348179 at a(101).

			a(3210) = 2020, because:
Moving 3 steps to the left from 3 gives: 3 -> 0 -> 1 -> 2.
Moving 2 steps to the left from 2 gives: 2 -> 3 -> 0.
Moving 1 step to the left from 1 gives: 1 -> 2.
Moving 0 steps to left from 0 gives: 0.

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

Cf. A336668 (fixed points), A348179 (to the right).

Cf. A139337, A346576, A347323.

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

a(n) = { my (d=digits(n)); fromdigits(vector(#d, k, d[1+(k-1-d[k])%#d])) } \\ Rémy Sigrist, Nov 17 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)))

cp's OEIS Frontend

A347323 Replace each nonzero digit d of n by (n mod d).

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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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Programs

Haskell

Mathematica

PARI

Python

Extensions

A349422 Replace each decimal digit d of n with the digit that is d steps to the left of d. Interpret the digits of n as a cycle: one step to the left from the first digit is considered to be the last.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Haskell

PARI

Python