A352450 -id:A352450 - cp's OEIS frontend

A352449 2^k appears in the binary expansion of a(n) iff 2^k appears in the binary expansion of n and k AND n = k (where AND denotes the bitwise AND operator).

0, 1, 0, 3, 0, 1, 4, 7, 0, 1, 0, 11, 0, 1, 4, 15, 0, 1, 0, 3, 16, 17, 20, 23, 0, 1, 0, 11, 16, 17, 20, 31, 0, 1, 0, 3, 0, 33, 4, 39, 0, 1, 0, 11, 0, 33, 4, 47, 0, 1, 0, 3, 16, 49, 20, 55, 0, 1, 0, 11, 16, 49, 20, 63, 0, 1, 0, 3, 0, 1, 68, 71, 0, 1, 0, 11, 0, 1

Offset: 0

Rémy Sigrist, Mar 16 2022

The idea is to keep the 1's in the binary expansion of a number whose positions are related in some way to that number.

			For n = 42:
- 42 = 2^5 + 2^3 + 2^1,
- 42 AND 5 = 0 <> 5,
- 42 AND 3 = 2 <> 3,
- 42 AND 1 = 0 <> 1,
- so a(42) = 0.

Rémy Sigrist, Table of n, a(n) for n = 0..8192
Index entries for sequences related to binary expansion of n

See A352450, A352451, A352452, A352458 for similar sequences.

Cf. A309274 (fixed points).

a(n) = { my (v=0, m=n, k); while (m, m-=2^k=valuation(m,2); if (bitand(n, k)==k, v+=2^k)); v }

a(n) <= n with equality iff n belongs to A309274.

A352451 2^k appears in the binary expansion of a(n) iff 2^k appears in the binary expansion of n and k+1 divides n.

Original entry on oeis.org

0, 1, 2, 1, 0, 1, 6, 1, 8, 1, 2, 1, 12, 1, 2, 5, 0, 1, 2, 1, 16, 5, 2, 1, 8, 17, 2, 1, 8, 1, 22, 1, 0, 1, 2, 1, 36, 1, 2, 5, 8, 1, 34, 1, 8, 5, 2, 1, 32, 1, 18, 1, 0, 1, 38, 17, 8, 1, 2, 1, 60, 1, 2, 5, 0, 1, 2, 1, 0, 5, 66, 1, 8, 1, 2, 1, 8, 65, 6, 1, 16, 1

Offset: 0

Rémy Sigrist, Mar 16 2022

The idea is to keep the 1's in the binary expansion of a number whose positions are related in some way to that number.

			For n = 42:
- 42 = 2^5 + 2^3 + 2^1,
- 5+1 divides 42,
- 3+1 does not divide 42,
- 1+1 divides 42,
- so a(42) = 2^5 + 2^1 = 34.

Rémy Sigrist, Table of n, a(n) for n = 0..8192
Index entries for sequences related to binary expansion of n

See A352449, A352450, A352452, A352458 for similar sequences.

a(n) = { my (v=0, m=n, k); while (m, m-=2^k=valuation(m,2); if (n%(k+1)==0, v+=2^k)); v }

a(n) <= n.

A352452 2^k appears in the binary expansion of a(n) iff 2^k appears in the binary expansion of n and k+1 does not divide n.

Original entry on oeis.org

0, 0, 0, 2, 4, 4, 0, 6, 0, 8, 8, 10, 0, 12, 12, 10, 16, 16, 16, 18, 4, 16, 20, 22, 16, 8, 24, 26, 20, 28, 8, 30, 32, 32, 32, 34, 0, 36, 36, 34, 32, 40, 8, 42, 36, 40, 44, 46, 16, 48, 32, 50, 52, 52, 16, 38, 48, 56, 56, 58, 0, 60, 60, 58, 64, 64, 64, 66, 68, 64

Offset: 0

Rémy Sigrist, Mar 16 2022

The idea is to keep the 1's in the binary expansion of a number whose positions are related in some way to that number.

			For n = 42:
- 42 = 2^5 + 2^3 + 2^1,
- 5+1 divides 42,
- 3+1 does not divide 42,
- 1+1 divides 42,
- so a(42) = 2^3 = 8.

Rémy Sigrist, Table of n, a(n) for n = 0..8192
Index entries for sequences related to binary expansion of n

See A352449, A352450, A352451, A352458 for similar sequences.

a(n) = { my (v=0, m=n, k); while (m, m-=2^k=valuation(m,2); if (n%(k+1), v+=2^k)); v }

a(n) <= n.

A352458 2^k appears in the binary expansion of a(n) iff 2^k appears in the binary expansion of n and k AND n = 0 (where AND denotes the bitwise AND operator).

Original entry on oeis.org

0, 1, 2, 1, 4, 5, 2, 1, 8, 1, 2, 1, 12, 5, 2, 1, 16, 17, 18, 17, 4, 5, 2, 1, 24, 17, 18, 17, 12, 5, 2, 1, 32, 1, 34, 1, 4, 5, 2, 1, 40, 1, 34, 1, 12, 5, 2, 1, 48, 17, 50, 17, 4, 5, 2, 1, 56, 17, 50, 17, 12, 5, 2, 1, 64, 65, 2, 1, 4, 5, 2, 1, 72, 65, 2, 1, 12

Offset: 0

Rémy Sigrist, Mar 17 2022

The idea is to keep the 1's in the binary expansion of a number whose positions are related in some way to that number.

			For n = 42:
- 42 = 2^5 + 2^3 + 2^1,
- 42 AND 5 = 0,
- 42 AND 3 = 2 <> 0,
- 42 AND 1 = 0,
- so a(42) = 2^5 + 2^1 = 34.

Rémy Sigrist, Table of n, a(n) for n = 0..8192
Index entries for sequences related to binary expansion of n

See A352449, A352450, A352451, A352452 for similar sequences.

Cf. A335702 (fixed points).

a(n) = { my (v=0, m=n, k); while (m, m-=2^k=valuation(m,2); if (bitand(n, k)==0, v+=2^k)); v }

a(n) <= n with equality iff n belongs to A335702.

a(n) = n - A309274(n).

cp's OEIS Frontend

A352449 2^k appears in the binary expansion of a(n) iff 2^k appears in the binary expansion of n and k AND n = k (where AND denotes the bitwise AND operator).

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A352451 2^k appears in the binary expansion of a(n) iff 2^k appears in the binary expansion of n and k+1 divides n.

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A352452 2^k appears in the binary expansion of a(n) iff 2^k appears in the binary expansion of n and k+1 does not divide n.

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A352458 2^k appears in the binary expansion of a(n) iff 2^k appears in the binary expansion of n and k AND n = 0 (where AND denotes the bitwise AND operator).

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