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A379785 For n >= 2, let b(n) = 1 if A379652(n) is 3 mod 4, 0 if A379652(n) is 1 mod 4; form the RUNS transform of {b(n), n >= 2}.

%I A379785 #13 Jan 11 2025 18:41:40
%S A379785 1,8,1,1,2,1,2,3,1,3,2,4,1,1,1,2,1,3,2,1,3,1,1,5,2,2,3,3,4,4,1,1,3,2,
%T A379785 1,2,1,3,1,6,1,3,2,1,2,2,1,1,1,2,1,1,1,4,2,1,1,1,1,15,1,3,3,1,5,1,1,3,
%U A379785 1,1,1,2,1,2,1,1,1,3,1,1,4,3,1,2,1,1,2,2,1,1,1,2,1,4,1,2,1,2,1,1,1,2,1,2,1,2,1,7,2,2
%N A379785 For n >= 2, let b(n) = 1 if A379652(n) is 3 mod 4, 0 if A379652(n) is 1 mod 4; form the RUNS transform of {b(n), n >= 2}.
%C A379785 Has the same relationship to A379652 as A379783 does to A379899. See A379783 for further information.
%H A379785 Michael De Vlieger, <a href="/A379785/b379785.txt">Table of n, a(n) for n = 1..10000</a>
%t A379785 nn = 400; c[_] := True; j = 2; q = 0; r = 1;
%t A379785 Rest@ Reap[Do[m = 2*j + 1;
%t A379785   While[Set[k, SelectFirst[FactorInteger[m][[All, 1]], c]];
%t A379785     ! IntegerQ[k], m = 2*m + 1];
%t A379785   c[k] = False; j = k;
%t A379785   If[# == r, q++, r = #; Sow[q]; q = 1] &[(Mod[k, 4] - 1)/2],
%t A379785 {n, nn}] ][[-1, 1]] (* _Michael De Vlieger_, Jan 11 2025 *)
%Y A379785 Cf. A379652, A379899, A379783.
%K A379785 nonn
%O A379785 1,2
%A A379785 _N. J. A. Sloane_, Jan 11 2025