OFFSET
1,11
COMMENTS
Record values:
1 * 1 = 1
21 * 15 = 315
81 * 17 = 1377
167 * 19 = 3173
169 * 33 = 5577
201 * 155 = 31155
633 * 283 = 179139
1011 * 743 = 751173
1101 * 833 = 917133
2001 * 1555 = 3111555
9091 * 4309 = 39173119
9901 * 32231 = 319119131
91001 * 34193 = 3111597193
100011 * 37927 = 3793117197
101001 * 58553 = 5913911553
200001 * 155555 = 31111155555
909091 * 431109 = 391917311919
990001 * 12121113 = 11999913991113
999001 * 31222311 = 31191119911311
... (above are exhaustive)
99990001 * 31122223111 = 3111911119991113111 (verified smallest)
9999900001 * 31112222231111 = 311119111119999111131111 (not verified smallest)
LINKS
FORMULA
a(n) = A061808(n)/(2n-1).
EXAMPLE
For n = 11, 2n-1 = 21, 21*15 = 315 which has all odd digits.
For m = 1 to 14, n*m listed are 21, 42, 63, 84, 105, 126, 147, 168, 189, 210, 231, 252, 273, 294, all of which contains at least one even digit.
MATHEMATICA
f[n_] := Block[{m = 1, nn = 2n -1, od = {1, 3, 5, 7, 9}}, While[ Union@ Join[od, IntegerDigits[m*nn]] != od, m += 2]; m]; Array[f, 75] (* Robert G. Wilson v, Dec 05 2017 *)
PROG
(PARI) isok(n, m) = {my(d = digits((2*n-1)*m)); #select(x->((x%2)==0), d) == 0; }
a(n) = {my(m=1); while (!isok(n, m), m++); m; } \\ Michel Marcus, Sep 24 2019
CROSSREFS
KEYWORD
AUTHOR
Yang Haoran, Dec 02 2017
STATUS
approved