A382702 -id:A382702 - cp's OEIS frontend

A382708 Number of triples (i,j,k), 1 <= i < j < k <= n such that A064413(i) < A064413(k) < A064413(j).

0, 0, 0, 0, 4, 4, 4, 14, 20, 39, 39, 39, 59, 97, 97, 97, 134, 162, 177, 260, 260, 280, 300, 360, 360, 423, 525, 694, 694, 722, 817, 895, 1129, 1129, 1162, 1254, 1546, 1546, 1615, 1751, 1856, 1925, 2326, 2326, 2436, 2546, 2625, 2704, 2783, 3061, 3104, 3196, 3415, 3458, 3458, 3699, 4439, 4439, 4590, 4890, 5725, 5725, 5842

Offset: 1

N. J. A. Sloane, Apr 04 2025

nonn

This is the number of occurrences of the pattern "132" in the first n terms of A064413.

			The first 5 terms of A064413 are 1, 2, 4, 6, 3, and at that point we can see four occurrences of the pattern "132", namely the triples 143, 163, 243, and 263, so a(5) = 4.

N. J. A. Sloane, Table of n, a(n) for n = 1..100

Cf. A064413, A152458, A382702-A382707.

A382703 Numbers k which appear "prematurely" in A064413, that is, k appears before the k-th term.

Original entry on oeis.org

4, 6, 9, 12, 10, 15, 18, 14, 21, 24, 20, 22, 33, 27, 30, 25, 35, 28, 39, 36, 32, 34, 51, 42, 38, 57, 45, 44, 46, 69, 48, 50, 52, 54, 56, 63, 60, 55, 65, 70, 58, 87, 66, 62, 93, 72, 68, 74, 111, 75, 78, 76, 80, 82, 123, 81, 84, 88, 86, 129, 90, 85, 95, 100, 92, 94, 141, 96, 98, 104, 102, 99, 105, 108, 106, 159, 114, 110, 112, 116

Offset: 1

N. J. A. Sloane, Apr 04 2025

nonn

a(n) = A064413(A382702(n)).

			4 appears in A064413 at the third term, so 4 is a term.

N. J. A. Sloane, Table of n, a(n) for n = 1..9296

Cf. A064413, A152458, A382702-A382708.

A382704 Indices k where b(k) < k, where b is the EKG sequence A064413.

Original entry on oeis.org

5, 10, 14, 17, 20, 27, 28, 33, 37, 43, 50, 57, 61, 67, 74, 78, 81, 89, 93, 100, 107, 115, 124, 128, 134, 138, 151, 160, 167, 171, 182, 189, 197, 203, 207, 210, 213, 216, 236, 253, 259, 264, 279, 287, 290, 297, 305, 314, 328, 336, 344, 363, 371, 377, 381, 401, 420, 430, 438, 444, 458, 462, 474, 487, 501, 510, 517, 530, 540, 549

Offset: 1

N. J. A. Sloane, Apr 04 2025

nonn

			A064413(5) = 3 < 5, so 5 is a term.

N. J. A. Sloane, Table of n, a(n) for n = 1..699

Cf. A064413, A152458, A382702-A382708.

A382707 a(n) = number of indices k, 1 <= k <= n, such that A064413(k) < k.

Original entry on oeis.org

0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 19

Offset: 1

N. J. A. Sloane, Apr 04 2025

nonn

N. J. A. Sloane, Table of n, a(n) for n = 1..10000

Cf. A064413, A152458, A382702-A382708.

A382705 Numbers k which are "delayed" in A064413, that is, k appears after the k-th term.

Original entry on oeis.org

3, 5, 7, 16, 11, 26, 13, 17, 19, 23, 49, 29, 31, 37, 41, 77, 43, 47, 91, 53, 59, 61, 121, 67, 71, 73, 79, 83, 89, 169, 97, 101, 103, 107, 109, 205, 209, 113, 127, 131, 137, 139, 149, 151, 289, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311

Offset: 1

N. J. A. Sloane, Apr 04 2025

nonn

a(n) = A064413(A382704(n)).

			3 only appears in A064413 at the fourth term, so 3 is a term.

N. J. A. Sloane, Table of n, a(n) for n = 1..699

Cf. A064413, A152458, A382702-A382708.

A382706 a(n) = number of indices k, 1 <= k <= n, such that A064413(k) > k.

Original entry on oeis.org

0, 0, 1, 2, 2, 3, 4, 4, 5, 5, 6, 7, 8, 8, 9, 10, 10, 11, 12, 12, 13, 14, 15, 16, 17, 18, 18, 18, 19, 20, 21, 22, 22, 23, 24, 25, 25, 26, 27, 27, 28, 29, 29, 30, 31, 32, 33, 34, 35, 35, 36, 37, 38, 39, 40, 41, 41, 42, 43, 44, 44, 45, 46, 46, 47, 48, 48, 49, 50, 51, 52, 53, 54, 54, 55, 56, 57, 57, 58, 59, 59, 60, 61, 62, 63, 64, 65, 66

Offset: 1

N. J. A. Sloane, Apr 04 2025

nonn

N. J. A. Sloane, Table of n, a(n) for n = 1..10000

Cf. A064413, A152458, A382702-A382708.

cp's OEIS Frontend

A382708 Number of triples (i,j,k), 1 <= i < j < k <= n such that A064413(i) < A064413(k) < A064413(j).

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A382703 Numbers k which appear "prematurely" in A064413, that is, k appears before the k-th term.

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A382704 Indices k where b(k) < k, where b is the EKG sequence A064413.

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A382707 a(n) = number of indices k, 1 <= k <= n, such that A064413(k) < k.

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A382705 Numbers k which are "delayed" in A064413, that is, k appears after the k-th term.

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Examples

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A382706 a(n) = number of indices k, 1 <= k <= n, such that A064413(k) > k.

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Author

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