A092213 -id:A092213 - cp's OEIS frontend

A330340 a(n) is the least k such that A092213(n) = k + reverse(k) (where reverse(k) is the binary reverse of k, A030101(k)).

0, 1, 2, 4, 3, 6, 5, 7, 10, 16, 9, 14, 11, 20, 18, 15, 32, 17, 22, 26, 21, 19, 30, 34, 23, 27, 44, 31, 38, 64, 33, 50, 46, 37, 54, 35, 68, 45, 62, 39, 66, 76, 51, 84, 47, 55, 74, 70, 92, 63, 128, 65, 98, 78, 86, 73, 106, 69, 102, 94, 67, 132, 77, 110, 85, 118

Offset: 0

Rémy Sigrist, Jan 21 2020

			For n = 3:
- A092213(3) = 5,
- 4 is the least k such that k + reverse(k) = 5,
- so a(3) = 4.

Rémy Sigrist, Table of n, a(n) for n = 0..7528
Rémy Sigrist, PARI program for A330340

Cf. A030101, A055944, A092213, A331585.

PARI
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a(n) + A030101(a(n)) = A092213(n).

a(n) <= A331585(n).

A331585 a(n) is the greatest k such that A092213(n) = k + reverse(k) (where reverse(k) is the binary reverse of k, A030101(k)).

Original entry on oeis.org

0, 1, 2, 4, 3, 8, 5, 7, 12, 16, 9, 14, 13, 20, 24, 15, 32, 17, 28, 26, 21, 25, 40, 48, 29, 27, 44, 31, 56, 64, 33, 50, 60, 41, 72, 49, 80, 45, 62, 57, 96, 88, 51, 84, 61, 59, 104, 112, 92, 63, 128, 65, 98, 120, 116, 73, 106, 81, 144, 124, 97, 160, 89, 122, 85

Offset: 0

Rémy Sigrist, Jan 21 2020

			For n = 5:
- A092213(5) = 9,
- 8 is the greatest k such that k + reverse(k) = 9,
- so a(5) = 8.

Rémy Sigrist, Table of n, a(n) for n = 0..7528
Rémy Sigrist, PARI program for A331585

Cf. A030101, A055944, A092213, A330340.

PARI
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See Links section.
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a(n) + A030101(a(n)) = A092213(n).

a(n) >= A330340(n).

A331587 Odd numbers of the form k * reverse(k) (where reverse(k) is the binary reversal of k, A030101(k)).

Original entry on oeis.org

1, 9, 25, 49, 81, 143, 225, 289, 441, 475, 667, 729, 961, 1089, 1517, 1715, 2025, 2223, 2279, 2601, 2867, 3245, 3969, 4225, 5329, 5589, 6499, 6853, 7225, 7875, 8023, 8383, 8649, 9559, 9801, 9919, 10179, 11449, 11845, 11875, 13653, 14161, 16129, 16641, 19865

Offset: 1

Rémy Sigrist, Jan 21 2020

A192775 is a subsequence.

			The binary representations of 11 and of 13 are "1011" and "1101", respectively, so 11*13 = 143 belongs to the sequence.

Rémy Sigrist, Table of n, a(n) for n = 1..8347

Cf. A030101, A092213, A192775, A331588, A331589.

is(n) = if (n%2, fordiv (n, d, if (d*fromdigits(Vecrev(binary(d)),2)==n, return (1)))); return (0)

A092214 In base 2: numbers n not of the form k + reverse(k) for any k.

Original entry on oeis.org

1, 4, 7, 8, 11, 12, 13, 16, 19, 20, 22, 23, 26, 28, 29, 31, 32, 36, 38, 39, 40, 41, 43, 46, 47, 48, 49, 50, 53, 55, 56, 58, 59, 60, 61, 64, 67, 68, 70, 71, 72, 73, 74, 76, 77, 79, 80, 82, 83, 86, 87, 88, 89, 91, 92, 94, 95, 97, 98, 100, 103, 104, 106, 107, 109, 110, 111, 112

Offset: 0

Klaus Brockhaus, Feb 25 2004

Base-2 analog of A067031 (base 10) and A091679 (base 4). Complement of A092213.

			13 is a term since 13 (decimal) = 1101 and there is no k such that k + reverse(k) = 1101 in base 2.

Cf. A092213, A067031, A091679.

cp's OEIS Frontend

A330340 a(n) is the least k such that A092213(n) = k + reverse(k) (where reverse(k) is the binary reverse of k, A030101(k)).

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A331585 a(n) is the greatest k such that A092213(n) = k + reverse(k) (where reverse(k) is the binary reverse of k, A030101(k)).

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A331587 Odd numbers of the form k * reverse(k) (where reverse(k) is the binary reversal of k, A030101(k)).

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PARI

A092214 In base 2: numbers n not of the form k + reverse(k) for any k.

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