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

1,2

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.

Links

Table of n, a(n) for n=1..9.

Rémy Sigrist, PARI program for A343522

Wikipedia, Factorial number system (Fractional values)

Index entries for sequences related to factorial base representation

Formula

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

Example

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

Prog

(PARI) See Links section.

Crossrefs

Cf. A294168, A279732.

Sequence in context: A014546 A068393 A032053 * A086542 A349893 A058181

Adjacent sequences: A343519 A343520 A343521 * A343523 A343524 A343525

Keyword

nonn,base,more,hard

Author

Rémy Sigrist, Apr 18 2021

Status

approved