A332995 -id:A332995 - cp's OEIS frontend

A332997 a(n) = A000120(A332995(n)).

0, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 3, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 3, 4, 1, 2, 1, 1, 2, 3, 2, 3, 1, 1, 2, 3, 1, 1, 2, 2, 2, 3, 2, 3, 3, 3, 4, 5, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 3, 4, 2, 2, 3, 3, 1, 2, 1, 2, 2, 2, 3, 4, 1, 2, 1, 1, 2, 3, 2, 3, 2, 2, 3, 4, 2, 2, 3, 3, 3, 4, 3, 4, 4, 4, 5, 6, 1, 2, 1, 1, 2, 3, 2, 3, 1, 1

Offset: 0

Antti Karttunen, Mar 05 2020

nonn

It seems that a(A055010(n)) = n for all n >= 0, and apart from n=1, A055010 seems to give the first occurrence of each n in this sequence.

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

Cf. A000120, A332817, A332897, A332995, A332998.

Cf. A052940, A055010.

A332997(n) = hammingweight(A332995(n));

PARI
```
A332997(n) = A332897(A332817(n));
```

a(n) = A000120(A332995(n)) = A332897(A332817(n)).

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

A332996 a(n) = A332896(A332817(n)).

Original entry on oeis.org

0, 0, 0, 1, 0, 0, 2, 2, 0, 1, 0, 0, 4, 5, 4, 5, 0, 0, 2, 2, 0, 1, 0, 0, 8, 8, 10, 11, 8, 8, 10, 10, 0, 1, 0, 0, 4, 5, 4, 5, 0, 0, 2, 2, 0, 1, 0, 0, 16, 17, 16, 17, 20, 20, 22, 23, 16, 17, 16, 16, 20, 21, 20, 21, 0, 0, 2, 2, 0, 1, 0, 0, 8, 8, 10, 11, 8, 8, 10, 10, 0, 1, 0, 0, 4, 5, 4, 5, 0, 0, 2, 2, 0, 1, 0, 0, 32, 32, 34, 35, 32, 32, 34, 34, 40, 41

Offset: 0

Antti Karttunen, Mar 05 2020

nonn

In contrast to similarly constructed A292274, 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. A292274, A332817, A332896, A332995, A332998.

Differs from a similarly constructed A292592 for the first time at n=511, where a(511) = 170, while A292592(511) = 171.

PARI
```
A332996(n) = A332896(A332817(n));
```

a(n) = A332896(A332817(n)).
a(n) = n - A332995(n) = n XOR A332995(n).
A000120(a(n)) = A332998(n).

cp's OEIS Frontend

A332997 a(n) = A000120(A332995(n)).

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A332996 a(n) = A332896(A332817(n)).

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Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

Formula