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

2, 14, 104, 2079, 21735, 3341624, 103488384, 6110171144

Offset

1,1

Comments

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.

a(9) > 2*10^11, if it exists.

Links

Table of n, a(n) for n=1..8.

Example

a(1) = 2 since A064547(2) = A064547(3) = 1.
a(2) = 14 since A064547(14) = A064547(15) = 2.

Mathematica

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]

Crossrefs

Cf. A064547, A343819.

Similar sequences: A045920, A052215, A075036, A093548, A115186.

Sequence in context: A295865 A355069 A293044 * A160780 A279737 A122680

Adjacent sequences: A343815 A343816 A343817 * A343819 A343820 A343821

Keyword

nonn,more

Author

Amiram Eldar, Apr 30 2021

Status

approved