A332996 -id:A332996 - cp's OEIS frontend

A332998 a(n) = A000120(A332996(n)).

0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 2, 3, 1, 1, 2, 2, 0, 1, 0, 0, 1, 2, 1, 2, 0, 0, 1, 1, 0, 1, 0, 0, 1, 2, 1, 2, 2, 2, 3, 4, 1, 2, 1, 1, 2, 3, 2, 3, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 2, 3, 1, 1, 2, 2, 0, 1, 0, 0, 1, 2, 1, 2, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 2, 3, 1, 1, 2, 2, 2, 3

Offset: 0

Antti Karttunen, Mar 05 2020

nonn

Antti Karttunen, Table of n, a(n) for n = 0..65537
Index entries for sequences related to binary expansion of n

Cf. A000120, A332817, A332898, A332996, A332997.

Cf. A086224.

A332998(n) = hammingweight(A332996(n));

PARI
```
A332998(n) = A332898(A332817(n));
```

a(n) = A000120(A332996(n)) = A332898(A332817(n)).
a(n) = A000120(n) - A332997(n).
Conjecture: for n >= 2, a(A086224(n-1)) = n, this being also the first occurrence of each n larger than 1.

A332995 a(n) = A332895(A332817(n)).

Original entry on oeis.org

0, 1, 2, 2, 4, 5, 4, 5, 8, 8, 10, 11, 8, 8, 10, 10, 16, 17, 16, 17, 20, 20, 22, 23, 16, 17, 16, 16, 20, 21, 20, 21, 32, 32, 34, 35, 32, 32, 34, 34, 40, 41, 40, 41, 44, 44, 46, 47, 32, 32, 34, 34, 32, 33, 32, 32, 40, 40, 42, 43, 40, 40, 42, 42, 64, 65, 64, 65, 68, 68, 70, 71, 64, 65, 64, 64, 68, 69, 68, 69, 80, 80, 82, 83, 80, 80, 82, 82, 88, 89, 88, 89, 92

Offset: 0

Antti Karttunen, Mar 05 2020

nonn

In contrast to similarly constructed A292271, this sequence can be computed directly from the binary expansion of n, without involving primes or their distribution at all.

Antti Karttunen, Table of n, a(n) for n = 0..16383
Antti Karttunen, Data supplement: n, a(n) computed for n = 0..65537
Index entries for sequences related to binary expansion of n

Cf. A292271, A332817, A332895, A332996, A332997.

Differs from a similarly constructed A292593 for the first time at n=511, where a(511) = 341, while A292593(511) = 340.

PARI
```
A332995(n) = A332895(A332817(n));
```

a(n) = A332895(A332817(n)).
a(n) = n - A332996(n) = n XOR A332996(n).
A000120(a(n)) = A332997(n).

cp's OEIS Frontend

A332998 a(n) = A000120(A332996(n)).

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A332995 a(n) = A332895(A332817(n)).

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