OFFSET
0,3
COMMENTS
The sequence is finite, the 18351st term being a(18350) = 41987 beyond which no number exists that has not occurred earlier that has all distinct digits and that 41987*a(n) has all distinct digits. The maximum term is a(18097) = 219087.
LINKS
Scott R. Shannon, Image of the 18351 terms. The green line is a(n) = n.
EXAMPLE
a(1) = 1 as 1 has one distinct digit and a(0)*1 = 0*1 = 0 which has one distinct digit 0.
a(10) = 10 as 10 has two distinct digits and a(9)*10 = 9*10 = 90 which has two distinct digits 9 and 0.
a(11) = 12 as 12 has two distinct digits and a(10)*12 = 10*12 = 120 which has three distinct digits. Note that 11 is the first skipped number as 11 has 1 as a duplicate digit.
a(16) = 19 as 19 has two distinct digits and a(15)*19 = 16*19 = 304 which has three distinct digits. Note that 17 and 18 are skipped as 16*17 = 272 while 16*18 = 288, both of which contain duplicate digits.
MATHEMATICA
Block[{a = {0}, k, m = 42000}, Do[k = 1; While[Nand[FreeQ[a, k], AllTrue[DigitCount[a[[-1]]*k], # < 2 &], AllTrue[DigitCount[k], # < 2 &]], If[k > m, Break[]]; k++]; If[k > m, Break[]]; AppendTo[a, k], {i, 76}]; a] (* Michael De Vlieger, Mar 11 2021 *)
CROSSREFS
KEYWORD
nonn,base,fini
AUTHOR
Scott R. Shannon, Mar 09 2021
EXTENSIONS
Offset corrected by N. J. A. Sloane, Jun 16 2021
STATUS
approved