A386482 -id:A386482 - cp's OEIS frontend

A387542 a(n) is the distance from the n-th term of A386482 to the nearest term of A386482 coprime to it.

0, 1, 2, 3, 2, 2, 4, 2, 2, 4, 2, 2, 2, 2, 3, 2, 3, 2, 5, 2, 3, 2, 3, 2, 3, 2, 3, 2, 2, 4, 2, 2, 2, 2, 3, 5, 4, 3, 5, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 4, 2, 2, 2, 2, 3, 5, 5, 6, 5, 4, 3, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 5, 6, 8, 8, 9, 11

Offset: 1

Rémy Sigrist, Sep 01 2025

In other words: a(n) is the least d >= 0 such that gcd(A386482(n), A386482(n - d)) = 1 or gcd(A386482(n), A386482(n + d)) = 1.

The sequence is well defined as A386482(1) = 1 is coprime to all terms of A386482.

			For n = 7: the GCD of A386482(7) = 12 and its neighboring terms are:
  d   A387542(7+d)  gcd(A387542(7), A387542(7+d))
  --  ------------  -----------------------------
  -4             4                              4
  -3             6                              6
  -2             3                              3
  -1             9                              3
   0            12                             12
   1            10                              2
   2             8                              4
   3            14                              2
   4             7                              1
The nearest coprime term, A387542(11) = 7, is at distance 4, so a(7) = 4.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program

Cf. A386482.

PARI
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\\ See Links section.
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A387544 Even terms of A386482, halved, in order of occurrence.

Original entry on oeis.org

1, 2, 3, 6, 5, 4, 7, 9, 8, 10, 15, 14, 13, 12, 11, 18, 17, 16, 19, 27, 26, 25, 24, 23, 22, 21, 20, 30, 29, 28, 34, 33, 32, 31, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 46, 47, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50

Offset: 1

Rémy Sigrist, Sep 01 2025

Each record in the sequence is followed by the smaller missing terms in descending order.

			The first terms, alongside the first terms of A386482, are:
  k   A386482(k)  n   a(n)
  --  ----------  --  ----
   1           1
   2           2   1     1
   3           4   2     2
   4           6   3     3
   5           3
   6           9
   7          12   4     6
   8          10   5     5
   9           8   6     4
  10          14   7     7
  11           7
  12          21
  13          18   8     9
  14          16   9     8
  15          20  10    10

Rémy Sigrist, Table of n, a(n) for n = 1..10306
Rémy Sigrist, PARI program

Cf. A386482, A387558.

PARI
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\\ See Links section.
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a(a(n)) = n.

A387558 Numbers k such that A386482(k) is even.

Original entry on oeis.org

2, 3, 4, 7, 8, 9, 10, 13, 14, 15, 19, 20, 21, 22, 23, 27, 28, 29, 30, 33, 34, 35, 36, 37, 38, 39, 40, 46, 47, 48, 53, 54, 55, 56, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 74, 75, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97

Offset: 1

Rémy Sigrist, Sep 02 2025

			A386482(46) = 60 is even, so 46 belongs to the sequence.

Rémy Sigrist, Table of n, a(n) for n = 1..10306
Rémy Sigrist, PARI program

Cf. A386482, A387544.

PARI
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\\ See Links section.
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A387544(n) = A386482(a(n)) / 2.

A387613 Numbers k such that A386482(k) and A386482(k+2) are coprime.

Original entry on oeis.org

1, 3, 6, 9, 11, 12, 14, 18, 22, 24, 26, 29, 31, 32, 41, 42, 44, 45, 47, 49, 50, 52, 55, 57, 58, 68, 70, 71, 73, 74, 76, 77, 98, 101, 102, 104, 109, 113, 115, 119, 122, 123, 124, 126, 137, 138, 142, 144, 174, 179, 187, 189, 192, 193, 196, 203, 205, 207, 234

Offset: 1

Rémy Sigrist, Sep 03 2025

For k > 1, A386482(k) and A386482(k+1) share a prime factor, however A386482(k) and A386482(k+2) may not share a prime factor. The present sequence lists those indexes.

			The first terms, alongside the first terms of A386482, are:
  k   A386482(k)  A386482(k+2)  n   a(n)
  --  ----------  ------------  --  ----
   1           1             4   1     1
   2           2             6
   3           4             3   2     3
   4           6             9
   5           3            12
   6           9            10   3     6
   7          12             8
   8          10            14
   9           8             7   4     9
  10          14            21
  11           7            18   5    11
  12          21            16   6    12
  13          18            20
  14          16            15   7    14
  15          20             5

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program

Cf. A386482, A387087.

PARI
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\\ See Links section.
```

A387634 Indices k such that s(k) is a prime p, s(k-1) = 2p, and s(k+1) = 3p, where s = A386482.

Original entry on oeis.org

5, 11, 24, 31, 57, 76, 236, 479, 1532, 7652, 82123, 129791, 274542, 419569, 3367328, 7002435, 7690249, 45355072

Offset: 1

Michael De Vlieger, Sep 04 2025

			Table of n, a(n), with a(n) = k, listing s(k) and its immediate neighbors:
 n  a(n) = k     s(k-1)      s(k)     s(k+1)
--------------------------------------------
 1         5         6         3          9
 2        11        14         7         21
 3        24        22        11         33
 4        31        38        19         57
 5        57        62        31         93
 6        76        94        47        141
 7       236       262       131        393
 8       479       634       317        951
 9      1532      1894       947       2841
10      7652      8654      4327      12981
11     82123     96182     48091     144273
12    129791    154474     77237     231711
13    274542    316978    158489     475467
14    419569    475466    237733     713199
15   3367328   3946174   1973087    5919261
16   7002435   6796442   3398221   10194663
17   7690249   8819038   4409519   13228557

Cf. A064413, A386482, A386483, A387072, A387076, A387077, A387522, A387523, A387524.

s = Import["https://oeis.org/A386482/b386482.txt", "Data"][[All, -1]]; m = Length[s]; t = TakeWhile[Import["https://oeis.org/A387077/b387077.txt", "Data"][[All, -1]], # <= m &]; Select[t, #1 == 2 #2 && #3 == 3 #2 & @@ s[[# - 1 ;; # + 1]] &] ]

a(18) from Chai Wah Wu, Sep 06 2025

A386488 Record high points in A386487.

Original entry on oeis.org

0, 1, 2, 3, 5, 9, 11, 25, 35, 64, 91, 108, 156, 194, 266, 471, 477, 538, 1308, 1485, 1945, 2479, 3256, 5328, 7247, 9008, 11566, 14859, 18714, 18815, 22031, 62149, 101919, 200924, 293629, 296260, 371947, 890616, 1177562, 2551932, 2827899, 3192227, 5538307, 6695946

Offset: 1

N. J. A. Sloane, Sep 01 2025

Needs a b-file!

Rémy Sigrist, PARI program

Cf. A386482, A387519-A387521.

r = -1; s = Import["https://oeis.org/A386482/b386482.txt","Data"][[All, -1]]; Reap[Do[If[# > r, r = #; Sow[#]] &[s[[n]] - n], {n, Length[s]}] ][[-1, 1]] (* Michael De Vlieger, Sep 01 2025 *)

PARI
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\\ See Links section.
```

More terms from Rémy Sigrist, Sep 02 2025

A387090 Distinct values of A387089.

Original entry on oeis.org

1, 2, 3, 5, 11, 13, 17, 23, 29, 41, 43, 89, 101, 109, 113, 151, 157, 163, 167, 223, 227, 229, 233, 239, 251, 257, 311, 313, 349, 383, 389, 443, 499, 503, 643, 653, 661, 673, 677, 683, 691, 709, 823, 827, 829, 839, 859, 863, 877, 881, 883, 887, 919, 937, 941, 971

Offset: 1

Rémy Sigrist, Aug 16 2025

These are the positive numbers that are the slowest to appear in A386482. Presumably they are all primes except for the initial 1. See A386484 for when they appear. - N. J. A. Sloane, Aug 16 2025

Rémy Sigrist, Table of n, a(n) for n = 1..1243
Rémy Sigrist, PARI program
Rémy Sigrist, C++ program

Cf. A386482, A386484, A387072, A387089.

\\ See Links section.
(C++) // See Links section.

Added a(1) = 1 and a comment. - N. J. A. Sloane, Aug 16 2025

A387519 Indices of record high points in A386487.

Original entry on oeis.org

1, 3, 4, 6, 7, 12, 19, 32, 58, 77, 145, 208, 237, 321, 369, 480, 838, 1290, 1533, 3031, 4003, 4965, 6900, 7653, 13365, 18980, 23022, 28225, 36034, 54189, 74152, 82124, 129792, 274543, 419570, 730075, 1679322, 1844372, 2469066

Offset: 1

N. J. A. Sloane, Sep 01 2025.

Needs a b-file!

Cf. A386482, A386487, A386488, A387520, A387521.

r = -1; s = Import["https://oeis.org/A386482/b386482.txt", "Data"][[All, -1]]; Reap[Do[If[# > r, r = #; Sow[n]] &[s[[n]] - n], {n, Length[s]}] ][[-1, 1]] (* Michael De Vlieger, Sep 01 2025 *)

More terms from Michael De Vlieger, Sep 01 2025

A387520 Record low points in A386487, negated.

Original entry on oeis.org

0, 2, 4, 12, 13, 31, 35, 50, 78, 97, 128, 204, 217, 241, 316, 337, 352, 381, 396, 407, 428, 439, 460, 471, 486, 495, 599, 600, 603, 605, 768, 778, 857, 927, 1057, 1252, 1318, 1919, 2244, 2524, 2554, 2809, 2866, 3384, 3896, 3930, 4373, 4668, 4709, 5446, 6006, 9236, 9289, 9514

Offset: 1

N. J. A. Sloane, Sep 01 2025.

In other words, record high points in -A386487.

Michael De Vlieger, Table of n, a(n) for n = 1..1129

Cf. A386482, A386487, A386488, A387519, A387521.

r = -1; s = Import["https://oeis.org/A386482/b386482.txt", "Data"][[All, -1]]; Reap[Do[If[# > r, r = #; Sow[#]] &[n - s[[n]]], {n, Length[s]}] ][[-1, 1]] (* Michael De Vlieger, Sep 01 2025 *)

A387521 Indices of record low points in A386487.

Original entry on oeis.org

1, 5, 11, 17, 24, 44, 52, 73, 115, 126, 189, 287, 320, 368, 453, 638, 639, 640, 641, 642, 643, 644, 645, 646, 647, 650, 652, 667, 674, 678, 809, 821, 996, 1016, 1206, 1425, 1497, 2020, 2425, 2637, 2747, 3006, 3017, 3541, 4597, 4649, 4680, 4867, 4876, 6105, 6247, 9513, 9662, 9795

Offset: 1

N. J. A. Sloane, Sep 01 2025

Michael De Vlieger, Table of n, a(n) for n = 1..1129

Cf. A386482, A386487, A386488, A387519, A387520.

cp's OEIS Frontend

A387542 a(n) is the distance from the n-th term of A386482 to the nearest term of A386482 coprime to it.

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A387544 Even terms of A386482, halved, in order of occurrence.

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A387558 Numbers k such that A386482(k) is even.

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A387613 Numbers k such that A386482(k) and A386482(k+2) are coprime.

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A387634 Indices k such that s(k) is a prime p, s(k-1) = 2*p, and s(k+1) = 3*p, where s = A386482.

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A386488 Record high points in A386487.

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PARI

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A387090 Distinct values of A387089.

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PARI

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A387519 Indices of record high points in A386487.

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Mathematica

A387634 Indices k such that s(k) is a prime p, s(k-1) = 2p, and s(k+1) = 3p, where s = A386482.