A379448 -id:A379448 - cp's OEIS frontend

A379446 a(n) is the number of ones in the binary expansion of 10^(10^n).

Original entry on oeis.org

2, 11, 105, 1163, 11683, 115979, 1161413, 11606847, 116093517, 1160951533, 11609679812, 116096181467, 1160963225086

Offset: 0

Hugo Pfoertner, Dec 26 2024

Cf. A000120, A011557, A118738, A153201, A379448.

PARI
```
a379446(n) = hammingweight(5^(10^n))
```

Conjectured: Limit_{n->oo} a(n)/10^n = log(5)/log(4). (A153201)

a(12) from Markus Sigg, Dec 28 2024

A379447 a(n) is the number of ones in the binary expansion of (n^n)^n.

Original entry on oeis.org

1, 1, 8, 1, 19, 27, 68, 1, 128, 105, 209, 120, 320, 266, 442, 1, 584, 524, 774, 476, 1006, 833, 1188, 477, 1486, 1248, 1746, 1066, 2068, 1733, 2365, 1, 2735, 2328, 3134, 1982, 3598, 3085, 4062, 1823, 4415, 3937, 5038, 3309, 5571, 4808, 6137, 1790, 6794, 5768, 7381

Offset: 1

Hugo Pfoertner, Dec 26 2024

			a(3) = 8: (3^3)^3 = 27^3 = 19683 = 100110011100011_2 which has 8 ones.

Cf. A000120, A002489, A379448.

Array[DigitCount[#^(#^2), 2, 1] &, 50] (* Michael De Vlieger, Dec 26 2024 *)

PARI
```
a379447(n) = hammingweight((n^n)^n)
```

a(2^k) = 1.

cp's OEIS Frontend

A379446 a(n) is the number of ones in the binary expansion of 10^(10^n).

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