A195608 - OEIS

%I #20 Dec 10 2019 05:22:38

%S 1,7,11,12,13,19,20,21,25,31,35,36,37,41,47,48,49,55,59,60,61,67,68,

%T 69,73,79,80,81,87,91,92,93,97,103,107,108,109,115,116,117,121,127,

%U 131,132,133,137,143,144,145,151,155,156,157,161,167,171,172,173,179

%N Numbers n such that Sum_{i=1..n} A(i) = A(n)*A(n+1)/4, where A(n) = A001969(n).

%C Conjectures: 1) there are only 3 different first differences 1,4,6; 2) the sequence contains either isolated series of terms, e.g., {1},{7},{25},{31},..., or series of 3 consecutive integers, e.g., {11,12,13}, {19,20,21}, etc.; 3)the first terms m of every series satisfy the condition A(m+1)-A(m-1)=5, where A(n)=A001969(n).

%H Amiram Eldar, <a href="/A195608/b195608.txt">Table of n, a(n) for n = 1..10000</a>

%t a = Select[Range[0, 1000], EvenQ[DigitCount[#, 2][[1]]] &]; t = {}; s = 0; Do[s = s + a[[n]]; If[s == a[[n]] a[[n + 1]]/4, AppendTo[t, n]], {n, Length[a] - 1}]; t (* _T. D. Noe_, Sep 23 2011 *)

%Y Cf. A001969, A195467.

%K nonn,base

%O 1,2

%A _Vladimir Shevelev_, Sep 21 2011