A339413 a(0) = 0; for n > 0, a(n) = a(n-1) if c0 == c1; a(n) = a(n-1) - c0 if c0 > c1; a(n) = a(n - 1) + c1 if c1 > c0, where c0 and c1 are respectively the number of 0's and 1's in the binary expansion of n.

0, 1, 1, 3, 1, 3, 5, 8, 5, 5, 5, 8, 8, 11, 14, 18, 14, 11, 8, 11, 8, 11, 14, 18, 15, 18, 21, 25, 28, 32, 36, 41, 36, 32, 28, 28, 24, 24, 24, 28, 24, 24, 24, 28, 28, 32, 36, 41, 37, 37, 37, 41, 41, 45, 49, 54, 54, 58, 62, 67, 71, 76, 81, 87, 81, 76, 71, 67, 62

Offset

0,4

Comments

The plot seems to have a fractal pattern.

The graph is similar to the Takagi (or blancmange) curve (which also involves bit counts). See A268289. - Kevin Ryde, Dec 04, 2020

Links

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

Mathematica

Block[{a = {0}}, Do[AppendTo[a, a[[-1]] + Which[#1 > #2, #1, #1 < #2, -#2, True, 0] & @@ DigitCount[i, 2]], {i, 68}]; a] (* Michael De Vlieger, Dec 07 2020 *)

Prog

(Python)
from collections import Counter
a = [0]
for i in range(1, 10000):
    counts = Counter(str(bin(i))[2:])
    if counts['0'] > counts['1']:
        a.append(a[-1] - counts['0'])
    elif counts['1'] > counts['0']:
        a.append(a[-1] + counts['1'])
    else:
        a.append(a[-1])
print(a)
(PARI) { for (n=0, 68, if (n==0, v=0, b=if (n, binary(n), [0]); c0=#b-c1=vecsum(b); if (c0>c1, v-=c0, c1>c0, v+=c1)); print1 (v", ")) } \\ Rémy Sigrist, Dec 25 2020

Crossrefs

Cf. A000120, A023416, A268289.

Sequence in context: A323556 A338329 A234587 * A114144 A050820 A261869

Adjacent sequences: A339410 A339411 A339412 * A339414 A339415 A339416

Keyword

easy,nonn,base

Author

Gioele Bertoncini, Dec 03 2020

Status

approved