A343522 Lexicographically least strictly increasing sequence such that, for any n > 0, Sum_{k = 1..n} 1/a(k) can be computed without carries in factorial base.

1, 2, 3, 7, 45, 631, 399168, 97044480, 55794106368

Offset: 1

Author

Rémy Sigrist, Apr 18 2021

Keywords

• nonn
• base
• more
• hard

Comments

This sequence is infinite as factorial base expansions of rational numbers are terminating.

In decimal base, we would end after four terms: 1, 2, 3, 6.

Examples

			The first terms, alongside the factorial base expansion of 1/a(n), are:
   n  a(n)  fact(1/a(n))
   -  ----  ------------------
   1     1  1
   2     2  0.1
   3     3  0.0 2
   4     7  0.0 0 3 2 0 6
   5    45  0.0 0 0 2 4
		

Links

• Rémy Sigrist, PARI program for A343522
• Wikipedia, Factorial number system (Fractional values)
• Index entries for sequences related to factorial base representation

Crossrefs

Cf. A294168, A279732.

Programs

PARI

See Links section.

Formula

Sum_{k = 1..n} 1/a(n) < 2.