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A076924 Smallest multiple of the n-th prime not containing any of its digits, or 0 if no such number exists. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A243428 A091376 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

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Last modified September 25 07:27 EDT 2021. Contains 347654 sequences. (Running on oeis4.)