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

1,2

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.

Links

Table of n, a(n) for n=1..25.

Example

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.

Sequence in context: A081868 A212103 A193652 * A092986 A295577 A325256

Adjacent sequences: A345366 A345367 A345368 * A345370 A345371 A345372

Keyword

nonn,base,easy

Author

Rémy Sigrist, Jun 16 2021

Status

approved