login
Starts of runs of 3 consecutive numbers with the same total binary weight of their divisors (A093653).
5

%I #12 Feb 04 2023 15:46:55

%S 3,242,243,1837,2361,3693,3728,6061,6457,9782,11181,11721,13855,15177,

%T 20017,22591,28021,31461,31887,33098,33993,38137,52016,52112,60321,

%U 76897,78542,78745,80461,108394,116017,119541,124453,125493,127117,127417,145369,151805,154113

%N Starts of runs of 3 consecutive numbers with the same total binary weight of their divisors (A093653).

%C Numbers k such that A093653(k) = A093653(k+1) = A093653(k+2).

%H Amiram Eldar, <a href="/A338453/b338453.txt">Table of n, a(n) for n = 1..10000</a>

%e 3 is a term since A093653(3) = A093653(4) = A093653(5) = 3.

%t f[n_] := DivisorSum[n, DigitCount[#, 2, 1] &]; s = {}; m = 3; fs = f /@ Range[m]; Do[If[Equal @@ fs, AppendTo[s, n - m]]; fs = Rest @ AppendTo[fs, f[n]], {n, m + 1, 155000}]; s

%t SequencePosition[Table[Total[DigitCount[Divisors[n],2,1]],{n,160000}],{x_,x_,x_}][[All,1]] (* _Harvey P. Dale_, Feb 04 2023 *)

%Y Cf. A093653.

%Y Subsequence of A338452.

%Y Similar sequences: A005238, A006073, A045939.

%K nonn,base

%O 1,1

%A _Amiram Eldar_, Oct 28 2020