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A187745 Numerators of Bernoulli numbers B(2^n). 0

%I #19 Sep 08 2022 08:45:56

%S 1,1,1,-1,-1,-3617,-7709321041217,

%T -106783830147866529886385444979142647942017

%N Numerators of Bernoulli numbers B(2^n).

%C Interestingly, the terms |a(n)| mod 100 show some regularity : 1, 1, 1, 1, 1, 17, 17, 17, 17, 69, 69, 69, 69, 69, 69, 69, 69, 53, 53, 53, 53, 53, ...

%C The only prime term up to a(20) is a(5)

%F a(n) = A164555(A131577(n))

%t A164555[n_] := If[n <= 2, 1, BernoulliB[n] // Numerator]; A131577[n_] := If[n == 0, 0, 2^(n-1)]; a[n_] := A164555[A131577[n]];

%t (* or *) a[n_] := n!*Coefficient[ Series[x/(1-Exp[-x]), {x, 0, 2^6}], x, Max[1, 2^(n-1)]] // Numerator; Table[a[n], {n, 0, 7}]

%o (Magma)

%o A164555:=func<n | n le 2 select 1 else Numerator(Bernoulli(n))>;

%o [A164555(2^(n-1)): n in [0..10]]; // _Bruno Berselli_, Jan 09 2013

%K sign,frac

%O 0,6

%A _Jean-Fran├žois Alcover_, Jan 03 2013

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Last modified July 13 11:56 EDT 2024. Contains 374282 sequences. (Running on oeis4.)