A233445 Start of record runs with lambda(k) = lambda(k+1) = ..., where lambda is Liouville's function A008836.

1, 2, 11, 17, 27, 140, 213, 1934, 13871, 38405, 171707, 200938, 389409, 1633357, 5460156, 8405437, 41983357, 68780189, 179376463, 130292951546, 393142151459, 2100234982892, 5942636062287

Offset: 1

Author

Charles R Greathouse IV, Dec 10 2013

Keywords

• nonn

Examples

			Lambda(1) = 1 is the first (record) run, so a(1) = 1.
Lambda(2) = lambda(3) = -1 is the second record run, so a(2) = 2.
Lambda(11) = lambda(12) = lambda(13) = -1 is the third record run, so a(3) = 11.
		

Crossrefs

Cf. A066793, A066794, A175201, A233459, A008836.

Programs

Mathematica

sz[n_] := Module[{t = LiouvilleLambda[n], k = n}, While[LiouvilleLambda[k++] == t]; k - n]; r = 0; Reap[For[n = 1, n <= 10^6, n++, t = sz[n]; If[t > r, r = t; Print[t, " ", n]; Sow[n]]]][[2, 1]] (* Jean-François Alcover, Oct 17 2016, adapted from PARI *)

PARI

L(n)=(-1)^bigomega(n);
sz(n)=my(t=L(n),k=n);while(L(k++)==t,);k-n
r=0;for(n=1,1e9,t=sz(n);if(t>r,r=t;print(t" "n)))