A223853 -id:A223853 - cp's OEIS frontend

A223900 Li estimate of the number of primes in successive power of two intervals [2^i, 2^(i+1)) for i >= 1.

2, 3, 4, 6, 9, 15, 25, 44, 78, 141, 256, 471, 873, 1625, 3040, 5713, 10774, 20385, 38684, 73603, 140374, 268298, 513811, 985763, 1894365, 3646034, 7027395, 13562528, 26207171, 50698756, 98183852, 190335311, 369325054, 717272497, 1394195117, 2712106284, 5279770660, 10285644688

Offset: 1

Brad Clardy, Mar 29 2013

nonn

The estimate is ceiling of Li(m) - Li(n) where m=2^(i+1) and n=2^i, i>=1.

Cf. A223853, A036378.

for i := 1 to 100 do
    x:=2^i;
    y:=2^(i+1);
    Ceiling(LogIntegral(y)-LogIntegral(x));
end for;

A356075 a(n) = floor(m), where li(m) = n and li is the logarithmic integral. We consider only real and positive m.

Original entry on oeis.org

1, 2, 4, 5, 7, 9, 11, 14, 17, 20, 23, 26, 29, 33, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 77, 81, 85, 90, 94, 99, 104, 108, 113, 118, 122, 127, 132, 137, 142, 147, 152, 157, 162, 167, 172, 178, 183, 188, 193, 198, 204, 209, 214, 220, 225, 231, 236, 242, 247, 253, 258

Offset: 1

Thomas Scheuerle, Jul 25 2022

nonn

We use for li(x) and x > 1 the Cauchy principal value of Integral_{0..x} dt/log(t). This is stated to prevent confusion with Li(x), which is often defined so that Li(x) = li(x) - li(2).

Cf. A052435, A089963, A096353, A223853, A337734, A337735.

cp's OEIS Frontend

A223900 Li estimate of the number of primes in successive power of two intervals [2^i, 2^(i+1)) for i >= 1.

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