A345369 Lexicographically earliest sequence of distinct positive integers such that for any n > 0, the product of the first n terms can be computed without carry in base 10.

1, 2, 3, 10, 11, 100, 101, 1000, 10000, 10001, 100000, 1000000, 10000000, 100000000, 100000001, 1000000000, 10000000000, 100000000000, 1000000000000, 10000000000000, 100000000000000, 1000000000000000, 10000000000000000, 10000000000000001, 100000000000000000

Offset: 1

Author

Rémy Sigrist, Jun 16 2021

Keywords

• nonn
• base
• easy

Comments

This sequence is a variant of A278742; here we multiply, there we add.

This sequence is the union of {2, 3}, A080176 and A011557.

Examples

			The first terms, alongside their product, are:
  n   a(n)   a(1) * ... * a(n)
  --  -----  ------------------
   1      1                   1
   2      2                   2
   3      3                   6
   4     10                  60
   5     11                 660
   6    100               66000
   7    101             6666000
   8   1000          6666000000
   9  10000      66660000000000
  10  10001  666666660000000000
		

Crossrefs

Cf. A080176, A011557.