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A342698 For any number n with binary expansion (b(1), b(2), ..., b(k)), the binary expansion of a(n) is (floor((b(k)+b(1)+b(2))/2), floor((b(1)+b(2)+b(3))/2), ..., floor((b(k-1)+b(k)+b(1))/2). 4
0, 1, 1, 3, 0, 7, 7, 7, 0, 9, 5, 15, 12, 15, 15, 15, 0, 17, 1, 19, 8, 27, 15, 31, 24, 25, 29, 31, 28, 31, 31, 31, 0, 33, 1, 35, 0, 35, 7, 39, 16, 49, 21, 55, 28, 63, 31, 63, 48, 49, 49, 51, 56, 59, 63, 63, 56, 57, 61, 63, 60, 63, 63, 63, 0, 65, 1, 67, 0, 67, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

This sequence is a variant of A342697; here we deal with bit triples in a "cyclic" binary representation of n.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Index entries for sequences related to binary expansion of n

FORMULA

a(n) + A342700(n) = A003817(n).

a(n) = n iff n belongs to A342699.

EXAMPLE

The first terms, in decimal and in binary, are:

  n   a(n)  bin(n)  bin(a(n))

  --  ----  ------  ---------

   0     0       0          0

   1     1       1          1

   2     1      10          1

   3     3      11         11

   4     0     100          0

   5     7     101        111

   6     7     110        111

   7     7     111        111

   8     0    1000          0

   9     9    1001       1001

  10     5    1010        101

  11    15    1011       1111

  12    12    1100       1100

  13    15    1101       1111

  14    15    1110       1111

  15    15    1111       1111

PROG

(PARI) a(n) = my (w=#binary(n)); sum(k=0, w-1, ((bittest(n, (k-1)%w)+bittest(n, k%w)+bittest(n, (k+1)%w))>=2) * 2^k)

CROSSREFS

Cf. A003817, A342697, A342699 (fixed points), A342700.

Sequence in context: A201900 A344387 A019970 * A239022 A343612 A198488

Adjacent sequences:  A342695 A342696 A342697 * A342699 A342700 A342701

KEYWORD

nonn,base

AUTHOR

Rémy Sigrist, Mar 18 2021

STATUS

approved

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Last modified May 28 05:47 EDT 2022. Contains 354112 sequences. (Running on oeis4.)