A346576 Let x run through the list of numbers with no zeros (A052382); replace each digit d of x by the digit (x mod d).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 4, 3, 2, 1, 10, 0, 12, 0, 10, 2, 16, 4, 12, 10, 20, 0, 12, 20, 0, 12, 26, 3, 10, 20, 31, 0, 10, 24, 35, 0, 14, 10, 20, 32, 42, 0, 12, 21, 32, 45, 10, 20, 30, 40, 50, 0, 14, 24, 36, 10, 20, 31, 42, 50, 64, 0, 16, 27, 10

Offset

1,13

Comments

Graph of the sequence generates a fractal-like image.

Links

Michel Marcus, Table of n, a(n) for n = 1..7380

Rakesh Khanna A, Graph of the sequence

Example

If x = 247 we get 132 as 247 mod 2 = 1, 247 mod 4 = 3, and 247 mod 7 = 2. As 247 is the 205th zeroless number,  a(205) =  132.

Mathematica

f[n_] := FromDigits @ Mod[n, IntegerDigits[n]]; f /@ Select[Range[100], !MemberQ[IntegerDigits[#], 0] &] (* Amiram Eldar, Jul 26 2021 *)

Prog

(C)
#include <stdio.h>
#define START 1
#define END 1000
int main(){
  unsigned int R, N, M, power_cntr;
  int mod1, mod2;
  for(N=START; N<=END; N++){
    R=N;
    M=0;
    power_cntr=1;
    while(R!=0){
      mod1=R%10;
      if(mod1==0) break;
      mod2=N%mod1;
      M+=mod2*power_cntr;
      power_cntr*=10;
      R=R/10; }
    if(mod1!=0) printf("%u %u\n", N, M); }
  return 0; }
(PARI) a(m) = my(d=digits(m)); fromdigits(Vec(apply(x->(m % x), d)));
apply(x->a(x), select(x->vecmin(digits(x)), [1..100])) \\ Michel Marcus, Jul 24 2021
(Python)
def f(k, digits): return int("".join(map(str, map(lambda x: k%x, digits))))
def aupton(terms):
    alst, k = [], 1
    while len(alst) < terms:
        s = str(k)
        if '0' not in s: alst.append(f(k, list(map(int, s))))
        k += 1
    return alst
print(aupton(73)) # Michael S. Branicky, Aug 22 2021

Crossrefs

Cf. A034838, A052382.

See A347323 for another version.

Sequence in context: A376252 A347323 A324471 * A122512 A128263 A241384

Adjacent sequences: A346573 A346574 A346575 * A346577 A346578 A346579

Keyword

nonn,base,look

Author

Rakesh Khanna A, Jul 24 2021

Status

approved