A328379 a(n) is the sum of the distinct numbers whose binary digits appear in order but not necessarily as consecutive digits in the binary representation of n.

0, 1, 3, 4, 7, 11, 12, 11, 15, 24, 31, 29, 28, 37, 33, 26, 31, 49, 66, 61, 71, 92, 85, 67, 60, 87, 103, 90, 77, 95, 78, 57, 63, 98, 133, 121, 150, 191, 177, 138, 151, 215, 254, 219, 197, 240, 199, 145, 124, 185, 237, 210, 235, 293, 262, 199, 165, 230, 263, 223

Offset

0,3

Links

Rémy Sigrist, Table of n, a(n) for n = 0..16384

Index entries for sequences related to binary expansion of n

Formula

A078823(n) <= a(n).

a(2^k) = 2^(k+1)-1 for any k >= 0.

a(2^k-1) = A000295(k+1) for any k >= 0.

Example

The first terms, alongside the binary representations of n as well as those of the numbers that appear in it, are:
  n   a(n)  bin(n)  {bin(s)}
  --  ----  ------  ----------------------------
   0     0       0  {0}
   1     1       1  {1}
   2     3      10  {0, 1, 10}
   3     4      11  {1, 11}
   4     7     100  {0, 1, 10, 100}
   5    11     101  {0, 1, 10, 11, 101}
   6    12     110  {0, 1, 10, 11, 110}
   7    11     111  {1, 11, 111}
   8    15    1000  {0, 1, 10, 100, 1000}
   9    24    1001  {0, 1, 10, 11, 100, 101, 1001}
  10    31    1010  {0, 1, 10, 11, 100, 101, 110, 1010}

Prog

(PARI) a(n, base=2) = { my (b=digits(n, base), s=[0]); for (k=1, #b, s = setunion(s, apply(o -> base*o+b[k], s))); vecsum(s) }

Crossrefs

Cf. A000295, A078823, A329873.

Sequence in context: A219188 A283428 A185506 * A080591 A291063 A047543

Adjacent sequences: A328376 A328377 A328378 * A328380 A328381 A328382

Keyword

nonn,base

Author

Rémy Sigrist, Nov 30 2019

Status

approved