A152458 -id:A152458 - cp's OEIS frontend

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

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.

A152519 Numbers k such that 2A064413(k) = 3k.

Original entry on oeis.org

4, 6, 12, 16, 34, 38, 58, 62

Offset: 1

Artur Jasinski, Dec 06 2008

The EKG sequence A064413 has 3 critical lines.
Points which belong to the critical lines:
(1) A064413(k) = k see A152458,
(3/2) 2*A064413(k) = 3*k see this sequence,
(1/2) 2*A064413(k) = k contains only 2 numbers: {10, 14}.
Only 12 and 16 in this sequence are not of the form 2*prime.
Because points are concentrated on the plot of EKG sequence near these 3 critical lines, the number of points belonging to critical lines is surprisingly low.
Conjecture: Number of points on 3 critical lines of EKG sequence is finite (and complete?). - Artur Jasinski, Dec 08 2008
a(9) > 10^5, if it exists. - Amiram Eldar, Oct 23 2024

Cf. A064413, A152458.

A268611 a(n) = A256417(n) - n.

Original entry on oeis.org

0, 2, 1, 0, 1, 0, 5, 0, 1, 0, -1, 6, 1, 0, -1, 8, -1, 2, 3, 2, 1, 5, 7, 1, 10, 2, -1, -2, -3, 6, 1, 2, 1, 0, 7, 2, 1, 0, 6, 0, 3, 4, 3, 2, 3, 4, 5, 6, 7, -1, 12, 8, 2, 11, 15, 2, 1, 0, 7, 2, 1, 0, 9, 0, 3, 8, 7, 6, 6, 8, 5, 8, 9, 8, 7, 5, 7, -1, 9, 6, 5, 4, 7

Offset: 1

Peter Kagey, Feb 08 2016

sign

A152458 is finite if and only if this sequence has a finite number of zeros.

Peter Kagey, Table of n, a(n) for n = 1..10000

Cf. A064413, A065519, A256417.

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.

A387088 Fixed points of A386482: numbers k such that A386482(k) = k.

Original entry on oeis.org

1, 2, 40, 49, 51, 98, 105, 3507, 3693, 4615, 5745, 6167, 32775, 102840, 106971, 2141244, 2419715, 4395321, 5855239, 6933770, 10440279, 20082095, 55680314, 95376809, 205626971, 240438171, 319745247, 346832939, 432366596, 877644251

Offset: 1

Rémy Sigrist, Aug 16 2025

			A386482(40) = 40, so 40 belongs to this sequence.

Rémy Sigrist, PARI program
Rémy Sigrist, C++ program

Cf. A152458, A386482.

PARI
```
\\ See Links section.
```

# uses generator/imports from A386482
def A387088_gen(): yield from (k for k, ak in enumerate(A386482_gen(), 1) if k == ak)
print(list(islice(A387088_gen(), 15))) # Michael S. Branicky, Aug 17 2025
(C++) // See Links section.

a(23)-a(30) from Rémy Sigrist, Sep 03 2025

cp's OEIS Frontend

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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A152519 Numbers k such that 2*A064413(k) = 3*k.

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A268611 a(n) = A256417(n) - n.

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

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A387088 Fixed points of A386482: numbers k such that A386482(k) = k.

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PARI

Python

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A152519 Numbers k such that 2A064413(k) = 3k.