cp's OEIS Frontend

A061807 Smallest positive multiple of n containing only even digits.

%I A061807 #22 Mar 03 2025 18:50:50
%S A061807 2,2,6,4,20,6,28,8,288,20,22,24,26,28,60,48,68,288,228,20,42,22,46,24,
%T A061807 200,26,486,28,406,60,62,64,66,68,280,288,222,228,468,40,82,42,86,44,
%U A061807 2880,46,282,48,686,200,204,208,424,486,220,224,228,406,826,60,244,62
%N A061807 Smallest positive multiple of n containing only even digits.
%H A061807 Paul Tek, <a href="/A061807/b061807.txt">Table of n, a(n) for n = 1..10000</a>
%F A061807 a(n) = n if n has only even digits, else 2n if n has only digits < 5, else 2*R(3k+3)+6*R(2k+2) if n = m*(10^k-1) with m = 1, 2, 4 or 8, else 10*a(n/5) if n = 5*(10^n-1). - _M. F. Hasler_, Mar 03 2025
%e A061807 a(7) = 28 because among the multiples of 7, that is, 7, 14, 21, 28,... 28 is the smallest multiple with only even digits.
%e A061807 a(16) = 48 is the first example where k(n) = a(n)/n > 1 is odd. The next examples are k(54) = 9, k(58) = 7, k(74) = 3, k(76) = 3, k(92) = 5, k(94) = 3, k(96) = 3, k(98) = 7. - _M. F. Hasler_, Mar 03 2025
%t A061807 Table[k = n; While[Length[Intersection[{1, 3, 5, 7, 9}, IntegerDigits[k]]] > 0, k = k + n]; k, {n, 100}] (* _T. D. Noe_, Jun 03 2013 *)
%t A061807 spme[n_]:=Module[{k=1},While[AnyTrue[IntegerDigits[k*n],OddQ],k++];k*n]; Array[spme,70] (* _Harvey P. Dale_, Mar 19 2024 *)
%o A061807 (PARI) apply( {A061807(n)=forstep(k=if(n%2,n*=2,n),oo,n, digits(k)%2||return(k))}, [1..99]) \\ _M. F. Hasler_, Mar 03 2025
%o A061807 (Python) A061807 = lambda n: next(n*k for k in range(1+n%2, 9<<99, 1+n%2)if not any(int(d)&1 for d in str(n*k))) # _M. F. Hasler_, Mar 03 2025
%Y A061807 Cf. A067044, A061808.
%Y A061807 Cf. A350538 (proper multiple).
%K A061807 base,nonn,easy
%O A061807 1,1
%A A061807 _Amarnath Murthy_, May 28 2001
%E A061807 Corrected and extended by Larry Reeves (larryr(AT)acm.org), May 29 2001