A338338 -id:A338338 - cp's OEIS frontend

A338349 Indices of records in A338338.

1, 2, 3, 4, 6, 8, 9, 13, 16, 17, 21, 25, 30, 51, 87, 99, 117, 173, 198, 211, 221, 233, 275, 402, 566, 572, 590, 625, 659, 667, 863, 900, 906, 1123, 1185, 1468, 1474, 1639, 1645, 1675, 1834, 1960, 2205, 2471, 2860, 3007, 3269, 3680, 3923, 4840, 4979, 5827, 5907, 6019

Offset: 1

N. J. A. Sloane, Oct 27 2020

nonn

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, C program for A338349

Cf. A338338-A338348.

C
```
See Links section.
```

A338339 Primes p in A338338 that occur at the start of a run of three terms in A338338 that are divisible by p.

Original entry on oeis.org

2, 5, 7, 11, 17, 31, 37, 41, 53, 67, 71, 79, 89, 101, 109, 131, 151, 173, 181, 197, 199, 211, 241, 257, 263, 277, 281, 293, 311, 347, 359, 383, 421, 431, 443, 487, 521, 523, 593, 607, 643, 659, 701, 709, 739, 809, 811, 827, 883, 971, 983, 1009, 1019, 1031, 1039, 1061, 1069, 1109

Offset: 1

N. J. A. Sloane, Oct 27 2020

nonn

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, C program for A338339

Cf. A338338-A338349.

C
```
See Links section.
```

A338340 Numbers k such that A338338(k) is a prime p that starts a run of three terms in A338338 that are divisible by p.

Original entry on oeis.org

2, 7, 11, 19, 38, 78, 82, 91, 125, 157, 161, 186, 206, 260, 290, 331, 377, 430, 453, 493, 502, 514, 601, 610, 619, 675, 684, 711, 744, 797, 822, 946, 1039, 1061, 1087, 1215, 1313, 1317, 1494, 1557, 1736, 1765, 1930, 1939, 2053, 2217, 2231, 2260, 2522, 2710, 2719, 2846, 2904

Offset: 1

N. J. A. Sloane, Oct 27 2020

nonn

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A338340

Cf. A338338-A338349.

PARI
```
See Links section.
```

A338342 Numbers k such that A338338(k) is a prime p in the middle of a run of three terms in A338338 that are divisible by p.

Original entry on oeis.org

5, 33, 42, 54, 73, 95, 120, 145, 152, 175, 190, 236, 264, 270, 294, 325, 335, 341, 372, 381, 387, 448, 474, 480, 552, 562, 568, 586, 605, 649, 655, 688, 739, 748, 768, 790, 811, 817, 921, 934, 973, 979, 1001, 1027, 1033, 1065, 1071, 1106, 1135, 1152, 1168, 1200, 1219, 1247, 1264

Offset: 1

N. J. A. Sloane, Oct 27 2020

nonn

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A338342

Cf. A338338-A338349.

PARI
```
See Links section.
```

A338344 Numbers k such that A338338(k) is a prime p that ends a run of three terms in A338338 that are divisible by p.

Original entry on oeis.org

429, 600, 796, 945, 1214, 1556, 3376, 3828, 4282, 4867, 5406, 6209, 6280, 6741, 6901, 7281, 7589, 7642, 7982, 8361, 8491, 8522, 8636, 8825, 8904, 9060, 9109, 9550, 9642, 9784, 10033, 10102, 10310, 11405, 11526, 11990, 12140, 12210, 12254, 12392, 12568, 13499, 13550

Offset: 1

N. J. A. Sloane, Oct 27 2020

nonn

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, C program for A338344

Cf. A338338-A338349.

C
```
See Links section.
```

A338348 Records in A338338.

Original entry on oeis.org

1, 2, 4, 6, 9, 10, 20, 28, 30, 40, 44, 56, 110, 170, 190, 248, 370, 424, 430, 470, 670, 710, 890, 1310, 1336, 1384, 1448, 1590, 1592, 2110, 2630, 2770, 2810, 3590, 3790, 3832, 3896, 4168, 4184, 4420, 5126, 6010, 7390, 8110, 9710, 10090, 10186, 12310, 13190, 15710, 16210

Offset: 1

N. J. A. Sloane, Oct 27 2020

nonn

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, C program for A338348

Cf. A338338-A338349.

C
```
See Links section.
```

A338440 a(n) is the greatest common divisor of A338338(n), A338338(n+1) and A338338(n+2).

Original entry on oeis.org

1, 2, 1, 3, 1, 1, 5, 2, 1, 1, 7, 2, 1, 3, 5, 2, 1, 1, 11, 2, 1, 3, 7, 2, 1, 3, 1, 11, 5, 2, 1, 13, 1, 3, 4, 1, 1, 17, 2, 1, 19, 1, 3, 5, 2, 7, 3, 1, 17, 5, 2, 1, 23, 1, 3, 2, 11, 1, 7, 5, 3, 1, 2, 13, 3, 1, 1, 5, 13, 2, 1, 29, 1, 3, 10, 1, 1, 31, 2, 1, 1, 37

Offset: 1

Rémy Sigrist, Oct 28 2020

nonn

No prime factor of a(n) divides A338338(n+3).

			a(4) = gcd(A338338(4), A338338(5), A338338(6)) = gcd(6, 3, 9) = 3.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, C program for A338440

Cf. A338338.

C
```
// See Links section.
```

gcd(a(n), A338338(n+3)) = 1.

A338449 a(n) is the radical of A338338(n).

Original entry on oeis.org

1, 2, 2, 6, 3, 3, 5, 10, 10, 2, 7, 14, 14, 6, 15, 30, 10, 2, 11, 22, 22, 6, 21, 42, 14, 6, 3, 33, 55, 110, 10, 26, 13, 39, 6, 6, 2, 17, 34, 34, 38, 19, 57, 15, 30, 70, 42, 21, 51, 85, 170, 10, 46, 23, 69, 6, 66, 22, 77, 35, 105, 15, 6, 26, 78, 39, 3, 5, 65

Offset: 1

Rémy Sigrist, Oct 28 2020

nonn

			For n = 9:
- A338338(9) = 20 = 2^2 * 5,
- so a(9) = 2 * 5 = 10.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A338449

Cf. A007947, A338338.

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

a(n) = A007947(A338338(n)).

A338450 Numbers k such that A338338(k) and A338338(k+1) are coprime.

Original entry on oeis.org

1, 6, 10, 18, 37, 67, 77, 81, 90, 124, 156, 160, 185, 205, 259, 289, 330, 376, 429, 452, 492, 501, 513, 600, 609, 618, 622, 674, 683, 710, 743, 796, 821, 945, 1038, 1060, 1086, 1214, 1312, 1316, 1493, 1556, 1735, 1764, 1929, 1938, 2052, 2216, 2230, 2259, 2521

Offset: 1

Rémy Sigrist, Oct 28 2020

nonn

			gcd(A338338(6), A338338(7)) = gcd(9, 5) = 1, so 6 belongs to the sequence.
gcd(A338338(2), A338338(3)) = gcd(2, 4) = 2, so 2 does not belong to the sequence.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, C program for A338450

Cf. A280774, A338338.

C
```
See Links section.
```

A338451 a(n) is the least positive number that does not appear among the first n terms of A338338.

Original entry on oeis.org

2, 3, 3, 3, 5, 5, 7, 7, 7, 7, 11, 11, 11, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 17, 17, 17, 17, 17, 19, 19, 19, 19, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 29

Offset: 1

Rémy Sigrist, Oct 28 2020

nonn

Conjecture: this sequence is unbounded (and A338338 is a permutation of the positive numbers).

			For n = 3:
- A338338(1) = 1,
- A338338(2) = 2,
- A338338(3) = 4,
- the number 3 is the least missing number,
- so a(3) = 3.

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, C program for A338451

Cf. A280740, A338338.

C
```
/* See Links section. */
```

cp's OEIS Frontend

A338349 Indices of records in A338338.

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C

A338339 Primes p in A338338 that occur at the start of a run of three terms in A338338 that are divisible by p.

Views

Author

Keywords

Links

Crossrefs

Programs

C

A338340 Numbers k such that A338338(k) is a prime p that starts a run of three terms in A338338 that are divisible by p.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

A338342 Numbers k such that A338338(k) is a prime p in the middle of a run of three terms in A338338 that are divisible by p.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

A338344 Numbers k such that A338338(k) is a prime p that ends a run of three terms in A338338 that are divisible by p.

Views

Author

Keywords

Links

Crossrefs

Programs

C

A338348 Records in A338338.

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Author

Keywords

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Programs

C

A338440 a(n) is the greatest common divisor of A338338(n), A338338(n+1) and A338338(n+2).

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Comments

Examples

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Programs

C

Formula

A338449 a(n) is the radical of A338338(n).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Formula

A338450 Numbers k such that A338338(k) and A338338(k+1) are coprime.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

C

A338451 a(n) is the least positive number that does not appear among the first n terms of A338338.