A349422 -id:A349422 - 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

A349423 Index of first occurrence of n in A348179, or -1 if n never appears.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1020, 11, 1023, 31, 1024, 51, 1063, 71, 1028, 91, 20, 21012, 12, 220035, 24, 20025, 26, 20074, 28, 220095, 230, 13, 300025, 33, 10413, 53, 300026, 73, 300085, 93, 40, 1041, 42, 3000461, 14, 5041, 46, 700451, 48, 9041, 520, 15

Offset: 0

Sebastian Karlsson, Nov 17 2021

			a(10) = 1020, because 1020 is the first number k such that A348179(k) = 10.
a(1111111110) = -1 (found by _Kevin Ryde_).

David A. Corneth, Table of n, a(n) for n = 0..10000 (first 453 terms from Sebastian Karlsson)

Cf. A336668, A348179, A349422.

def A348179(n):
    s, l = str(n), len(str(n))
    return int("".join(s[(i + int(s[i])) % l] for i in range(l)))
terms = {}
for n in range(0, 3000462): # 3000462 to get all terms of the data-section without -1s.
    if (k := A348179(n)) not in terms: terms[k] = n
for n in range(0, 52):
    try: print(terms[n], end=", ")
    except: print(-1, end=", ") # These -1s are conjectured.

A354719 Replace each even digit in n with the digit to its left.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 11, 11, 13, 11, 15, 11, 17, 11, 19, 2, 11, 22, 33, 42, 55, 62, 77, 82, 99, 33, 31, 33, 33, 33, 35, 33, 37, 33, 39, 4, 11, 24, 33, 44, 55, 64, 77, 84, 99, 55, 51, 55, 53, 55, 55, 55, 57, 55, 59, 6, 11, 26, 33, 46, 55, 66, 77

Offset: 0

Gavin Lupo, Jun 03 2022

If the leftmost digit in n is even, wrap around and replace it with the rightmost digit in n (see example).

			n    =  4 2 7 8 1
        ^ ^   ^      even digits,
a(n) =  1 4 7 7 1    to their left in n

Michael De Vlieger, Table of n, a(n) for n = 0..10000
Gavin Lupo, Logarithmic scatterplot of (n, a(n)) for n = 1..10000

Cf. A139337, A348179, A349422.

Array[FromDigits@ Map[If[EvenQ@ #1, #2, #1] & @@ # &, Transpose@ {#, RotateRight[#, 1]}] &@ IntegerDigits[#] &, 67] (* Michael De Vlieger, Jun 19 2022 *)

prec(d, k) = k--; if (! k, k = #d); k;
a(n) = my(d=digits(n), v=d); for (k=1, #d, if (!(d[k] % 2), v[k] = d[prec(d,k)])); fromdigits(v); \\ Michel Marcus, Jun 04 2022

def a(n):
    digits = list(map(int, str(n)))
    out = (d if d%2 else digits[i-1] for i, d in enumerate(digits))
    return int("".join(map(str, out)))
print([a(n) for n in range(68)]) # Michael S. Branicky, Jun 04 2022

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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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A349423 Index of first occurrence of n in A348179, or -1 if n never appears.

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A354719 Replace each even digit in n with the digit to its left.

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