A061807 Smallest positive multiple of n containing only even digits.

2, 2, 6, 4, 20, 6, 28, 8, 288, 20, 22, 24, 26, 28, 60, 48, 68, 288, 228, 20, 42, 22, 46, 24, 200, 26, 486, 28, 406, 60, 62, 64, 66, 68, 280, 288, 222, 228, 468, 40, 82, 42, 86, 44, 2880, 46, 282, 48, 686, 200, 204, 208, 424, 486, 220, 224, 228, 406, 826, 60, 244, 62

Offset: 1

Author

Amarnath Murthy, May 28 2001

Keywords

• base
• nonn
• easy

Examples

			a(7) = 28 because among the multiples of 7, that is, 7, 14, 21, 28,... 28 is the smallest multiple with only even digits.
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
		

Links

• Paul Tek, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A067044, A061808.

Cf. A350538 (proper multiple).

Programs

Mathematica

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 *)
spme[n_]:=Module[{k=1},While[AnyTrue[IntegerDigits[k*n],OddQ],k++];k*n]; Array[spme,70] (* Harvey P. Dale, Mar 19 2024 *)

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

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

Formula

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

Extensions

Corrected and extended by Larry Reeves (larryr(AT)acm.org), May 29 2001