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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

%I #8 Apr 20 2021 02:40:59

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

%N 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.

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

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

%H Rémy Sigrist, <a href="/A343522/a343522.gp.txt">PARI program for A343522</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Factorial_number_system#Fractional_values">Factorial number system (Fractional values)</a>

%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>

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

%e The first terms, alongside the factorial base expansion of 1/a(n), are:

%e n a(n) fact(1/a(n))

%e - ---- ------------------

%e 1 1 1

%e 2 2 0.1

%e 3 3 0.0 2

%e 4 7 0.0 0 3 2 0 6

%e 5 45 0.0 0 0 2 4

%o (PARI) See Links section.

%Y Cf. A294168, A279732.

%K nonn,base,more,hard

%O 1,2

%A _Rémy Sigrist_, Apr 18 2021