cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A387079 Least prime factor of A386482(n).

Original entry on oeis.org

1, 2, 2, 2, 3, 3, 2, 2, 2, 2, 7, 3, 2, 2, 2, 3, 5, 5, 2, 2, 2, 2, 2, 11, 3, 3, 2, 2, 2, 2, 19, 3, 2, 2, 2, 2, 2, 2, 2, 2, 5, 3, 3, 13, 5, 2, 2, 2, 7, 3, 3, 17, 2, 2, 2, 2, 31, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 3, 3, 23, 2, 2, 47, 3, 2, 2, 2, 2, 2, 2, 2, 2
Offset: 1

Views

Author

Michael De Vlieger, Aug 18 2025

Keywords

Comments

Minimum absolute difference |s(n-1)-s(n)|, since GCD(s(n-1),s(n)) > 1, where s = A386482.

Links

Crossrefs

Cf. A020639, A386482, A387073, A387074, A387075.

Programs

  • Mathematica
    Block[{c, j, k, p, m, nn}, nn = 120; c[] := False; m[] := 1; j = 2; c[1] = c[2] = True; {1, 2}~Join~Reap[Do[If[PrimePowerQ[j], Set[{p, k, m}, {#1, #1^(#2 - 1), #1^(#2 - 1)}] & @@ FactorInteger[j][[1]]; While[And[c[k*p], k != 0], k--];vIf[k == 0, k = m; While[c[k*p], k++]]; k *= p, k = j - 1; While[And[Or[c[k], CoprimeQ[j, k]], k != 1], k--]; If[k == 1, k += j; While[Or[c[k], CoprimeQ[j, k]], k++] ] ]; Sow[FactorInteger[k][[1, 1]] ]; Set[{c[k], j}, {True, k}], {n, 3, nn}]][[-1, 1]] ]

Formula

a(n) = A020639(A386482(n)).
a(n) <= |A386075(n-1)|.
a(m) = s(m) = A387073(i) for m = A387074(i).

A387087 GCD of pairs of consecutive terms of the sequence A386482.

Original entry on oeis.org

1, 2, 2, 3, 3, 3, 2, 2, 2, 7, 7, 3, 2, 4, 5, 5, 5, 5, 2, 2, 2, 2, 11, 11, 3, 9, 2, 2, 2, 19, 19, 3, 2, 2, 2, 2, 2, 2, 2, 5, 5, 3, 13, 13, 5, 2, 2, 7, 7, 3, 17, 17, 2, 2, 2, 31, 31, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 5, 3, 23, 23, 2, 47, 47, 3, 2, 2, 2, 2, 2
Offset: 1

Views

Author

Rémy Sigrist, Aug 16 2025

Keywords

Examples

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

Links

Crossrefs

Cf. A073734, A386482.

Programs

  • PARI
    \\ See Links section.

Formula

a(n) = gcd(A386482(n), A386482(n+1)).

A387089 Smallest number missing in the sequence A386482 after n terms.

Original entry on oeis.org

2, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 11, 11, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 17, 17, 17, 17, 17, 17, 17, 17, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23
Offset: 1

Views

Author

Rémy Sigrist, Aug 16 2025

Keywords

Examples

			The first terms, alongside the first terms of A386482, are:
  n   a(n)  A386482(n)
  --  ----  ----------
   1     2           1
   2     3           2
   3     3           4
   4     3           6
   5     5           3
   6     5           9
   7     5          12
   8     5          10
   9     5           8
  10     5          14
  11     5           7
  12     5          21
  13     5          18
  14     5          16
  15     5          20
  16     5          15
  17    11           5

Links

Crossrefs

Cf. A137847, A386482.

Programs

  • PARI
    \\ See Links section.

A387103 For any n >= 2, a(n) is the number of positive values k < A386482(n-1) missing from the first n-1 terms of A386482 such that gcd(k, A386482(n-1)) != 1.

Original entry on oeis.org

0, 0, 0, 1, 0, 0, 2, 2, 0, 1, 0, 2, 2, 0, 2, 1, 0, 0, 5, 3, 3, 1, 1, 0, 1, 0, 2, 2, 0, 1, 0, 6, 10, 8, 7, 6, 4, 2, 3, 1, 0, 1, 1, 0, 2, 4, 2, 1, 0, 1, 1, 0, 3, 3, 1, 1, 0, 8, 16, 11, 9, 11, 7, 7, 6, 3, 3, 2, 1, 0, 1, 1, 0, 0, 1, 0, 17, 31, 22, 20, 28, 24, 16
Offset: 2

Views

Author

Rémy Sigrist, Aug 16 2025

Keywords

Comments

This sequence gives essentially the number of candidates for A386482(n) that are less than A386482(n-1).

Examples

			The first terms, alongside A386482(n) and the corresponding k's, are:
  n   a(n)  A386482(n)  Candidates
  --  ----  ----------  --------------------
   1  N/A            1  N/A
   2     0           2  {}
   3     0           4  {}
   4     0           6  {}
   5     1           3  {3}
   6     0           9  {}
   7     0          12  {}
   8     2          10  {8, 10}
   9     2           8  {5, 8}
  10     0          14  {}
  11     1           7  {7}
  12     0          21  {}
  13     2          18  {15, 18}
  14     2          16  {15, 16}
  15     0          20  {}
  16     2          15  {5, 15}
  17     1           5  {5}
  18     0          25  {}
  19     0          30  {}
  20     5          28  {22, 24, 26, 27, 28}

Links

Crossrefs

Cf. A386482.

Programs

  • PARI
    \\ See Links section.

Formula

a(n) = 0 iff A386482(n) > A386482(n-1).

A387081 Indices k such that lpf(s(k-1)) does not divide abs(s(k) - s(k-1)), where s = A386482 and lpf = A020639.

Original entry on oeis.org

5, 11, 16, 17, 24, 31, 41, 44, 49, 52, 57, 70, 73, 76, 100, 103, 106, 115, 121, 125, 126, 139, 144, 176, 189, 194, 205, 207, 236, 275, 287, 299, 310, 320, 363, 368, 431, 453, 479, 615, 634, 647, 650, 652, 661, 662, 667, 674, 678, 684, 737, 785, 788, 800, 801
Offset: 1

Views

Author

Michael De Vlieger, Aug 19 2025

Keywords

Comments

A387077 appears to be a proper subset, apart from its first term. This is to say the indices of primes in A386482, except for A387077(1) = 2, appear in this sequence.

Examples

			Table of n, a(n), relating these to s = A386482, where v = abs(s(k) - s(k-1)), p = lpf(a(n)-1):
 n a(n)=k   v   p
-----------------
 1     5    3   2
 2    11    7   2
 3    16    5   2
 4    17   10   3
 5    24   11   2
 6    31   19   2
 7    41    5   2
 8    44   26   3
 9    49    7   2
10    52   34   3
11    57   31   2
12    70   15   2
22   139   19   2

Links

Crossrefs

Cf. A020639, A386482, A387077, A387079.

Programs

  • Mathematica
    s = Import["https://oeis.org/A386482/b386482.txt","Data"][[ ;; , -1]]; j = 1; {2}~Join~Reap[Do[If[! Divisible[Abs[j - s[[n]]], FactorInteger[j][[1, 1]] ], Sow[n]]; j = s[[n]], {n, 2, Length[s]}] ][[-1, 1]]

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

Views

Author

Rémy Sigrist, Aug 16 2025

Keywords

Examples

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

Links

Crossrefs

Cf. A152458, A386482.

Programs

  • PARI
    \\ See Links section.
  • Python
    # 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.

Extensions

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

A387104 Split A386482 into maximal runs of consecutive decreasing terms; a(n) is the length of the n-th run.

Original entry on oeis.org

1, 1, 1, 2, 1, 3, 2, 3, 3, 1, 6, 2, 3, 2, 10, 3, 5, 3, 5, 13, 3, 1, 2, 25, 2, 1, 3, 1, 1, 6, 7, 1, 3, 12, 4, 2, 33, 1, 1, 10, 6, 1, 11, 29, 51, 23, 10, 48, 61, 24, 26, 168, 1, 2, 2, 9, 1, 3, 2, 7, 2, 2, 6, 104, 15, 2, 1, 1, 2, 3, 3, 1, 1, 4, 11, 5, 159, 9, 1
Offset: 1

Views

Author

Rémy Sigrist, Aug 16 2025

Keywords

Examples

			The first terms, alongside the corresponding runs, are:
  n   a(n)  Corresponding run
  --  ----  --------------------------------------
   1     1  1
   2     1  2
   3     1  4
   4     2  6, 3
   5     1  9
   6     3  12, 10, 8
   7     2  14, 7
   8     3  21, 18, 16
   9     3  20, 15, 5
  10     1  25
  11     6  30, 28, 26, 24, 22, 11
  12     2  33, 27
  13     3  36, 34, 32
  14     2  38, 19
  15    10  57, 54, 52, 50, 48, 46, 44, 42, 40, 35
  16     3  45, 39, 13

Links

Crossrefs

Cf. A386482, A387103.

Programs

  • PARI
    \\ See Links section.

Formula

A387103(1 + Sum_{k = 1..n} a(k)) = 0 for any n > 0.

A387522 Index of first term in A386482 that is divisible by the n-th prime.

Original entry on oeis.org

2, 4, 8, 10, 23, 21, 28, 30, 37, 47, 56, 67, 63, 61, 75, 94, 88, 86, 80, 119, 117, 135, 131, 174, 166, 162, 160, 156, 154, 150, 200, 235, 229, 227, 217, 215, 209, 270, 266, 260, 254, 252, 242, 240, 297, 295, 314, 354, 350, 348, 344, 338, 336, 326, 428, 422, 416, 414, 408, 404, 402, 392, 378, 374, 372, 478, 464, 458, 608, 606, 602
Offset: 1

Views

Author

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

Keywords

Links

Crossrefs

Cf. A386482, A386483, A387072, A387076.

Programs

  • Mathematica
    Block[{p, s}, p[A386482/b386482.txt%22,%20%22Data%22%5D%5B%5BAll,%20-1%5D%5D;%20Do%5BMap%5BIf%5Bp%5B%23%5D%20==%200,%20Set%5Bp%5B%23%5D,%20n%5D%5D%20&,%20FactorInteger%5Bs%5B%5Bn%5D%5D%5D%5B%5B;;%20,%201%5D%5D%5D,%20%7Bn,%20Length%5Bs%5D%7D%5D;%20TakeWhile%5BArray%5Bp%5BPrime%5B%23%5D%5D%20&,%20120%5D,%20%23%20%3E%200%20&%5D%20%5D%20(*%20_Michael%20De%20Vlieger">] := 0; s = Import["https://oeis.org/A386482/b386482.txt", "Data"][[All, -1]]; Do[Map[If[p[#] == 0, Set[p[#], n]] &, FactorInteger[s[[n]]][[;; , 1]]], {n, Length[s]}]; TakeWhile[Array[p[Prime[#]] &, 120], # > 0 &] ] (* _Michael De Vlieger, Sep 03 2025 *)

A387523 Primes in the order in which they first divide a term of A386482.

Original entry on oeis.org

2, 3, 5, 7, 13, 11, 17, 19, 23, 29, 31, 43, 41, 37, 47, 67, 61, 59, 53, 73, 71, 83, 79, 113, 109, 107, 103, 101, 97, 89, 127, 157, 151, 149, 139, 137, 131, 193, 191, 181, 179, 173, 167, 163, 199, 197, 211, 251, 241, 239, 233, 229, 227, 223, 313, 311, 307, 293, 283, 281, 277, 271, 269, 263, 257, 337, 331, 317, 467, 463, 461, 457
Offset: 1

Views

Author

N. J. A. Sloane, Sep 03 2025

Keywords

Comments

Conjecture: if c is the first term in A386482 that is divisible by a prime p > 2, then c = 2*p.

Examples

			11 first divides A386482(23), but 13 first divides A386482(21), so 13 precedes 11 in this sequence.

Links

Crossrefs

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

Programs

  • Mathematica
    Block[{p, s}, p[A386482/b386482.txt%22,%20%22Data%22%5D%5B%5BAll,%20-1%5D%5D;%20Rest@%20Reap%5BDo%5BMap%5BIf%5Bp%5B%23%5D%20==%200,%20Set%5Bp%5B%23%5D,%20n%5D;%20Sow%5B%23%5D%5D%20&,%20FactorInteger%5Bs%5B%5Bn%5D%5D%20%5D%5B%5B;;%20,%201%5D%5D%5D,%20%7Bn,%20Length%5Bs%5D%7D%5D%20%5D%5B%5B-1,%201%5D%5D%20%5D%20(*%20_Michael%20De%20Vlieger">] := 0; s = Import["https://oeis.org/A386482/b386482.txt", "Data"][[All, -1]]; Rest@ Reap[Do[Map[If[p[#] == 0, Set[p[#], n]; Sow[#]] &, FactorInteger[s[[n]] ][[;; , 1]]], {n, Length[s]}] ][[-1, 1]] ] (* _Michael De Vlieger, Sep 03 2025 *)

A387524 Primes p with property that in A386482 they are immediately preceded by 2*p and immediately followed by 3*p.

Original entry on oeis.org

3, 7, 11, 19, 31, 47, 131, 317, 947, 4327, 48091, 77237, 158489, 237733, 1973087, 3398221, 4409519
Offset: 1

Views

Author

N. J. A. Sloane, Sep 03 2025

Keywords

Comments

This is in marked contrast to the EKG sequence A064413, where all primes > 2 have this property.

Crossrefs

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

Extensions

More terms from Michael De Vlieger, Sep 03 2025
Previous Showing 11-20 of 32 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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