A076924 Smallest multiple of the n-th prime not containing any of its digits, or 0 if no such number exists.

4, 6, 10, 14, 22, 26, 34, 38, 46, 58, 62, 111, 82, 86, 188, 106, 118, 244, 134, 284, 146, 158, 166, 267, 388, 2222, 824, 428, 327, 226, 508, 262, 548, 278, 2086, 302, 628, 489, 334, 692, 358, 362, 382, 772, 2364, 2388, 633, 446, 454, 458, 466, 478, 3856, 4769

Offset

1,1

Comments

a(n) = 0 if and only if prime(n) contains all decimal digits with the possible exception of 0. Otherwise, if n > 3 and p=prime(n) does not contain the nonzero digit k, the repdigit (10^m-1)*k/9 is a multiple of p where m is the order of 10 mod p. - Robert Israel, Jul 21 2020

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = A074157(prime(n)). - Robert Israel, Jul 21 2020

Maple

f:= proc(n) local p, k, r, D;
  D:= convert(convert(n, base, 10), set);
  for k from 2 to 10^(1+ilog10(n)) do
    r:= k*n;
    if convert(convert(r, base, 10), set) intersect D = {} then return r fi
  od;
  error ("search failed for n=%1", n)
end proc:
seq(f(ithprime(i)), i=1..100); # Robert Israel, Jul 21 2020

Mathematica

smp[p_]:=Module[{k=2}, While[ContainsAny[IntegerDigits[k*p], IntegerDigits[ p]], k++]; k*p]; Table[smp[p], {p, Prime[Range[60]]}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 19 2019 *)

Crossrefs

Cf. A074157, A076925.

Sequence in context: A091376 A363134 A100484 * A103801 A141247 A049632

Adjacent sequences: A076921 A076922 A076923 * A076925 A076926 A076927

Keyword

base,nonn

Author

Amarnath Murthy, Oct 17 2002

Extensions

Corrected and extended by Ray Chandler, Feb 11 2005

Status

approved