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%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
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