

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).


2



0, 1, 2, 15, 16, 5, 30, 511, 512, 33, 10, 47, 240, 61, 1022, 65535, 65536, 1025, 66, 271, 80, 21, 94, 1535, 7680, 481, 122, 495, 8176, 2045, 131070, 33554431, 33554432, 131073, 2050, 8207, 528, 133, 542, 8703, 2560, 161, 42, 175, 752, 189, 3070, 196607, 983040
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OFFSET

0,3


COMMENTS

This sequence has similarities with A001196: here we square the length of each run of consecutive equal bits, there we double it.


LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..16383
Index entries for sequences related to binary expansion of n


FORMULA

a(n) = A322403(n, n).
a(n) >= n with equality iff n belongs to A000975.
a(2^n) = 2^(n^2) for any n >= 0.
a(2^n  1) = 2^(n^2)  1 for any n >= 0.
A005811(a(n)) = A005811(n).


MATHEMATICA

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*)


PROG

(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)


CROSSREFS

Cf. A000975, A001196, A005811, A322403.
Sequence in context: A077518 A196242 A102101 * A163480 A037312 A267711
Adjacent sequences: A322146 A322147 A322148 * A322150 A322151 A322152


KEYWORD

nonn,base


AUTHOR

Rémy Sigrist, Nov 28 2018


STATUS

approved



