A326300 Steinhaus sums.

2, 6, 8, 16, 18, 22, 24, 40, 42, 46, 48, 56, 58, 62, 64, 96, 98, 102, 104, 112, 114, 118, 120, 136, 138, 142, 144, 152, 154, 158, 160, 224, 226, 230, 232, 240, 242, 246, 248, 264, 266, 270, 272, 280, 282, 286, 288, 320, 322, 326, 328, 336, 338, 342, 344, 360, 362, 366, 368

Offset

1,1

Links

Table of n, a(n) for n=1..59.

Sandor Csörgö, Gordon Simons, On Steinhaus' resolution of the St. Petersburg paradox, Probab. Math. Statist. 14 (1993), 157--172. MR1321758 (96b:60017). See p. 163 and Table 1 p. 171.

Formula

a(n) = Sum_{k>=1} floor(n/2^k + 1/2)*2^k.

a(n) = 2 * A006520(n-1).

Prog

(PARI) a(n) = sum(k=1, 1+log(n)\log(2), floor(n/2^k+1/2)*2^k);
(Python)
def a(n):
    s = 0
    for k in range(1, n.bit_length()+1):
        s += ((n + (1 << (k-1))) >> k) << k
    return s
print([a(n) for n in range(1, 60)]) # Darío Clavijo, Aug 24 2024

Crossrefs

Cf. A000523 (log_2(n)), A006520.

Sequence in context: A336896 A306906 A174658 * A266074 A191822 A238549

Adjacent sequences: A326297 A326298 A326299 * A326301 A326302 A326303

Keyword

nonn

Author

Michel Marcus, Oct 17 2019

Status

approved