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

Author

Amarnath Murthy, Oct 17 2002

Keywords

• base
• nonn

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

Crossrefs

Cf. A074157, A076925.

Programs

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 *)

Formula

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

Extensions

Corrected and extended by Ray Chandler, Feb 11 2005