cp's OEIS Frontend

A322149 In the binary representation of n, replace each run of k 0's (or 1's) with k^2 0's (or 1's).

%I A322149 #14 Dec 07 2018 12:15:24
%S A322149 0,1,2,15,16,5,30,511,512,33,10,47,240,61,1022,65535,65536,1025,66,
%T A322149 271,80,21,94,1535,7680,481,122,495,8176,2045,131070,33554431,
%U A322149 33554432,131073,2050,8207,528,133,542,8703,2560,161,42,175,752,189,3070,196607,983040
%N A322149 In the binary representation of n, replace each run of k 0's (or 1's) with k^2 0's (or 1's).
%C A322149 This sequence has similarities with A001196: here we square the length of each run of consecutive equal bits, there we double it.
%H A322149 Rémy Sigrist, <a href="/A322149/b322149.txt">Table of n, a(n) for n = 0..16383</a>
%H A322149 <a href="http://oeis.org/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A322149 a(n) = A322403(n, n).
%F A322149 a(n) >= n with equality iff n belongs to A000975.
%F A322149 a(2^n) = 2^(n^2) for any n >= 0.
%F A322149 a(2^n - 1) = 2^(n^2) - 1 for any n >= 0.
%F A322149 A005811(a(n)) = A005811(n).
%t A322149 squareList[v_] := Flatten[ConstantArray[v, {Length[v]}]]; a[n_] := FromDigits[ Flatten[squareList /@ Split[IntegerDigits[n, 2]]], 2]; Array[a, 60, 0] (* _Amiram Eldar_, Dec 07 2018*)
%o A322149 (PARI) a(n) = if (n==0, 0, my (b=n%2, k=valuation(n+b,2)); (a(n\2^k) + b) * 2^(k^2) - b)
%Y A322149 Cf. A000975, A001196, A005811, A322403.
%K A322149 nonn,base
%O A322149 0,3
%A A322149 _Rémy Sigrist_, Nov 28 2018