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

Author

Michel Marcus, Oct 17 2019

Keywords

• nonn

Links

• 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.

Crossrefs

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

Programs

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

Formula

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

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