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A227361 If n is even, then a(n) = n + bitsum(n), else a(n) = n - bitsum(n), where bitsum(n) is the count of binary 1's in n, A000120. 3
0, 0, 3, 1, 5, 3, 8, 4, 9, 7, 12, 8, 14, 10, 17, 11, 17, 15, 20, 16, 22, 18, 25, 19, 26, 22, 29, 23, 31, 25, 34, 26, 33, 31, 36, 32, 38, 34, 41, 35, 42, 38, 45, 39, 47, 41, 50, 42, 50, 46, 53, 47, 55, 49, 58, 50, 59, 53, 62, 54, 64, 56, 67, 57, 65, 63, 68, 64, 70, 66, 73, 67, 74, 70, 77, 71, 79, 73, 82, 74, 82, 78, 85, 79, 87, 81, 90, 82, 91, 85 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

I gathered together some interesting statistics for this seq A227361:

Within the first 200000001 members of this sequence, only 70 were repeated 4 times, and then only when n > 2 million. None were repeated 5 times.

The first value to become repeated 3 times is 50, occurring at indexes (n=) 46, 48, and 55.

The first value to become repeated 4 times is 2097170, occurring at indexes (n=) 2097150, 2097166, 2097168, and 2097175.

The total count of those only occuring once is 96226727, or about 48.11 %.

Total count of those repeated 2 times is 45055158.

Total count of those repeated 3 times is 4554221, or about 2.28 %.

Total count of those repeated 4 times is 70  (extremely low).

Repeatedly applying this BitStoneA(v) function to values in a recursive (nested) style has shown that only 21 starting values shall become zero. These are those values: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 23, 27. All other values shall cycle forever in small loops.

274877906962 is the smallest number that occurs 5 times. - Donovan Johnson, Jul 27 2013

LINKS

Andres M. Torres, Table of n, a(n) for n = 0..10000

FORMULA

a(n) = n + (-1)^n sum_{j = 1 .. floor(log_2(n)) + 1} (floor(n/2^j + 1/2)) - floor(n/2^j)). - Alonso del Arte, Jul 08 2013, based on one of Hieronymus Fischer's formulas for A000120.

EXAMPLE

a(0) = 0 because 0 is even, so 0 + bitsum(0) = 0.

a(1) = 0 because 1 is odd, so 1 - bitsum(1) = 0.

a(2) = 3 because 2 is even, so 2 + bitsum(2) = 3.

a(3) = 1 because 3 is odd, so 3 - bitsum(3) = 1.

MATHEMATICA

Table[n + (-1)^n DigitCount[n, 2, 1], {n, 0, 127}] (* Alonso del Arte, Jul 08 2013 *)

PROG

(Blitz3D code)

Each a(n) is generated simply as follows:  a(n) = BitStoneA(n)

Function BitStoneA(n)

         If  (n Mod 2)              ;; if is odd

                 Return n-bitsum(n)

         Else                       ;; if is even

                 Return n+bitsum(n)

         End If

End Function

--- Or, If n is even, then return n+A000120(n), else return n-A000120(n), where A000120(n) = bitsum(n)

(PARI) a(n)=n+(-1)^(n%2)*hammingweight(n) \\ Charles R Greathouse IV, Jul 09 2013

CROSSREFS

Cf. A000120, A055938, A010061, A010062.

Sequence in context: A097062 A324894 A200498 * A318726 A212641 A195835

Adjacent sequences:  A227358 A227359 A227360 * A227362 A227363 A227364

KEYWORD

nonn,easy,base

AUTHOR

Andres M. Torres, Jul 08 2013

STATUS

approved

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Last modified June 17 17:41 EDT 2019. Contains 324196 sequences. (Running on oeis4.)