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A343818 a(n) is the least number k such that k and k+1 both have n Fermi-Dirac factors (A064547).

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%I A343818 #9 Nov 21 2021 05:07:17
%S A343818 2,14,104,2079,21735,3341624,103488384,6110171144
%N A343818 a(n) is the least number k such that k and k+1 both have n Fermi-Dirac factors (A064547).
%C A343818 Since the number of infinitary divisors of k is A037445(k) = 2^A064547(k), a(n) is also the least number k such that k and k+1 both have 2^n infinitary divisors.
%C A343818 a(9) > 2*10^11, if it exists.
%e A343818 a(1) = 2 since A064547(2) = A064547(3) = 1.
%e A343818 a(2) = 14 since A064547(14) = A064547(15) = 2.
%t A343818 fd[1] = 0; fd[n_] := Plus @@ DigitCount[FactorInteger[n][[;;,2]], 2, 1]; seq[m_] := Module[{s = Table[0, {m}], c = 0, n = 1, fd1, fd2}, fd1=fd[n]; While[c < m, fd2 = fd[++n]; If[fd1 == fd2 && fd1 <= m && s[[fd1]] == 0, s[[fd1]] = n-1; c++]; fd1=fd2]; s]; seq[5]
%Y A343818 Cf. A064547, A343819.
%Y A343818 Similar sequences: A045920, A052215, A075036, A093548, A115186.
%K A343818 nonn,more
%O A343818 1,1
%A A343818 _Amiram Eldar_, Apr 30 2021