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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.

User: Michael De Vlieger

Michael De Vlieger's wiki page.

Michael De Vlieger has authored 869 sequences. Here are the ten most recent ones:

A387081 Indices k such that lpf(s(k)) != lpf(s(k-1)), where s = A386482 and lpf = A020736.

Original entry on oeis.org

2, 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. This is to say the indices of primes in A386482 appear in this sequence.

Examples

			Table of n, a(n), relating these to s = A387482:
 n a(n)=k  s(k-1) s(k) s(k+1)
-----------------------------
 1     2     1     2     4
 2     5     6     3     9
 3    11    14     7    21
 4    16    20    15     5
 5    17    15     5    25
 6    24    22    11    33
 7    31    38    19    57
 8    41    40    35    45
 9    44    39    13    65
10    49    56    49    63
11    52    51    17    68
12    57    62    31    93
23   139   152   171   165

Links

Crossrefs

Cf. A020736, 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]]

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).

A387062 a(n) = number of wiggly permutations |W_n|.

Original entry on oeis.org

1, 1, 2, 5, 14, 51, 176, 807, 3232, 17449, 78384, 479897, 2366248, 16041147, 85534176, 631596455, 3602770400, 28633529345, 173300710720, 1469070416505, 9373542317760, 84152568224563, 563142033172480, 5323835899152567, 37206559614499840, 368667413713034441, 2681213937595142656
Offset: 0

Views

Author

Michael De Vlieger, Aug 15 2025

Keywords

Comments

Permutation P over [n] is said to be wiggly given the following two items hold for all pairs of values of the form (2*j-1, 2*j):
For upward order: if 2*j-1 appears before 2*j in P, then interposing terms are larger.
For downward order: if 2*j occurs before 2*j-1 in P, then interposing terms are smaller.

Examples

			W_2 = {12, 21},
W_3 = {123, 132, 213, 312, 321},
W_4 = {1234, 1243, 1342, 1423, 1432, 2134, 2143, 3412, 3421, 4123, 4132, 4213, 4312, 4321}.

Links

Crossrefs

Cf. A344654.

Extensions

a(17)-a(26) from Alois P. Heinz, Aug 17 2025

A387080 a(1)=1, a(2)=3; thereafter a(n) is either the greatest number k < a(n-1) not already used such that gcd(k, a(n-1)) > 1, or if no such k exists then a(n) is the smallest number k > a(n-1) not already used such that gcd(k, a(n-1)) > 1.

Original entry on oeis.org

1, 3, 6, 4, 2, 8, 10, 5, 15, 12, 9, 18, 16, 14, 7, 21, 24, 22, 20, 25, 30, 28, 26, 13, 39, 36, 34, 32, 38, 19, 57, 54, 52, 50, 48, 46, 44, 42, 40, 35, 45, 33, 27, 51, 17, 68, 66, 64, 62, 60, 58, 56, 49, 63, 69, 23, 92, 90, 88, 86, 84, 82, 80, 78, 76, 74, 72, 70
Offset: 1

Views

Author

Geoffrey Caveney and Michael De Vlieger, Aug 16 2025

Keywords

Comments

This is a variant of A386482 that begins with 1,3 instead of 1,2.

Links

Crossrefs

Cf. A386482.

Programs

  • Mathematica
    Block[{c, j, k, m, p, r, nn},
  nn = 2^12; c[] := False; m[] := 1; j = 2; c[1] = c[2] = True; r = 1;
  {1}~Join~Monitor[Most@ 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--];
        If[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++] ] ];
    If[Mod[j, 2] == Mod[k, 2], r++, Sow[r]; r = 1];
    Set[{c[k], j}, {True, k}], {n, 3, nn}] ][[-1, 1]], n] ]

A387078 Run lengths of A386482(n) mod 2 == n mod 2.

Original entry on oeis.org

1, 3, 2, 4, 2, 3, 3, 5, 3, 4, 2, 8, 5, 3, 4, 4, 2, 11, 4, 2, 2, 22, 16, 5, 3, 1, 2, 12, 6, 31, 14, 4, 3, 8, 3, 28, 2, 37, 14, 10, 12, 9, 2, 41, 7, 61, 24, 24, 2, 134, 71, 51, 97, 3, 2, 127, 69, 39, 15, 64, 55, 56, 26, 100, 37, 32, 40, 33, 2, 440, 107, 196, 391
Offset: 1

Views

Author

Michael De Vlieger, Aug 15 2025

Keywords

Comments

Let S = A386482.
Beginning with S(481) = 948, there are 100 consecutive even terms in S. Starting with S(730076) = 1026330, there are 100869 consecutive even terms in S.

Examples

			S begins as follows, grouping odd terms in brackets [], and even in parentheses ():
   [1], (2, 4, 6), [3, 9], (12, 10, 8, 14), [7, 21], (18, 16, 20), [15, 5, 25], ...
This sequence takes run lengths in the order they appear, therefore a(1) = 1, a(2) = 3, a(3) = 2, a(4) = 4, a(5) = 2, etc. Hence a(n) for odd n pertains to run lengths of odd terms in S, while a(n) for even n pertains to run lengths of even terms in same.

Links

Crossrefs

Cf. A386482.

Programs

  • Mathematica
    Block[{c, j, k, m, p, r, nn},
  nn = 2^12; c[] := False; m[] := 1; j = 2; c[1] = c[2] = True; r = 1;
  {1}~Join~Monitor[Most@ 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--];
        If[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++] ] ];
    If[Mod[j, 2] == Mod[k, 2], r++, Sow[r]; r = 1];
    Set[{c[k], j}, {True, k}], {n, 3, nn}] ][[-1, 1]], n] ]

A387077 Indices of prime terms in A386482.

Original entry on oeis.org

2, 5, 11, 17, 24, 31, 44, 52, 57, 73, 76, 115, 126, 144, 189, 207, 236, 287, 310, 320, 368, 453, 479, 652, 667, 674, 678, 684, 809, 821, 832, 837, 996, 1016, 1034, 1088, 1206, 1289, 1425, 1497, 1532, 2020, 2026, 2053, 2079, 2425, 2442, 2445, 2522, 2542, 2578, 2637
Offset: 1

Views

Author

Michael De Vlieger, Aug 15 2025

Keywords

Links

Crossrefs

Cf. A386482, A387076.

Programs

  • Mathematica
    Block[{c, j, k, m, p, r, nn},
  nn = 3000; c[] := False; m[] := 1; j = 2; c[1] = c[2] = True; r = 1;
  {1}~Join~Monitor[Most@ 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--];
        If[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++] ] ];
    If[PrimeQ[k], Sow[n]];
    Set[{c[k], j}, {True, k}], {n, 3, nn}] ][[-1, 1]], n] ]

A387076 Primes in the order in which they appear in A386482.

Original entry on oeis.org

2, 3, 7, 5, 11, 19, 13, 17, 31, 23, 47, 37, 29, 59, 61, 79, 131, 83, 107, 103, 127, 137, 317, 53, 67, 71, 73, 211, 41, 43, 97, 263, 139, 89, 347, 379, 149, 457, 173, 179, 947, 101, 109, 191, 647, 181, 269, 271, 431, 433, 439, 113, 557, 193, 569, 449, 197, 151
Offset: 1

Views

Author

Michael De Vlieger, Aug 15 2025

Keywords

Links

Crossrefs

Cf. A386482, A387077.

Programs

  • Mathematica
    Block[{c, j, k, m, p, r, nn},
  nn = 3000; c[] := False; m[] := 1; j = 2; c[1] = c[2] = True; r = 1;
  {1}~Join~Monitor[Most@ 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--];
        If[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++] ] ];
    If[PrimeQ[k], Sow[k]];
    Set[{c[k], j}, {True, k}], {n, 3, nn}] ][[-1, 1]], n] ]

A387075 First differences of A386482.

Original entry on oeis.org

1, 2, 2, -3, 6, 3, -2, -2, 6, -7, 14, -3, -2, 4, -5, -10, 20, 5, -2, -2, -2, -2, -11, 22, -6, 9, -2, -2, 6, -19, 38, -3, -2, -2, -2, -2, -2, -2, -2, -5, 10, -6, -26, 52, -5, -2, -2, -7, 14, -12, -34, 51, -2, -2, -2, -31, 62, -3, -2, -2, -2, -2, -2, -2, -2, -2
Offset: 1

Views

Author

Michael De Vlieger, Aug 15 2025

Keywords

Links

Crossrefs

Cf. A386482.

Programs

  • Mathematica
    Block[{c, j, k, m, p, r, nn},
  nn = 120; c[] := False; m[] := 1; j = 2; c[1] = c[2] = True; r = 0;
  {1, 2}~Join~Monitor[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--];
        If[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[k - j]; Set[{c[k], j}, {True, k}], {n, 3, nn}] ][[-1, 1]], n] ]

A387074 Indices of record high points in A386482.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 10, 12, 18, 19, 25, 27, 30, 32, 45, 53, 58, 75, 77, 116, 124, 127, 143, 145, 190, 196, 197, 208, 237, 288, 311, 321, 369, 454, 480, 685, 833, 838, 1035, 1089, 1207, 1290, 1426, 1498, 1533, 2080, 2668, 2785, 2888, 3031, 3782, 4003, 4965, 5748
Offset: 1

Views

Author

Michael De Vlieger, Aug 15 2025

Keywords

Links

Crossrefs

Cf. A386482, A387073.

Programs

  • Mathematica
    Block[{c, j, k, m, p, r, nn},
  nn = 6000; c[] := False; m[] := 1; j = 2; c[1] = c[2] = True; r = 0;
  {1, 2}~Join~Monitor[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--];
        If[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++] ] ];
    If[k > r, r = k; Sow[n]];
    Set[{c[k], j}, {True, k}], {n, 3, nn}] ][[-1, 1]], n] ]

A387073 Record high points in A386482.

Original entry on oeis.org

1, 2, 4, 6, 9, 12, 14, 21, 25, 30, 33, 36, 38, 57, 65, 68, 93, 94, 141, 148, 150, 174, 177, 236, 244, 247, 260, 316, 393, 415, 428, 515, 635, 685, 951, 1055, 1067, 1315, 1388, 1516, 1639, 1828, 1903, 1969, 2841, 3235, 3342, 3414, 3592, 4516, 4936, 5948, 7444, 7652
Offset: 1

Views

Author

Michael De Vlieger, Aug 15 2025

Keywords

Links

Crossrefs

Cf. A386462, A387074.

Programs

  • Mathematica
    Block[{c, j, k, m, p, r, nn},
  nn = 6000; c[] := False; m[] := 1; j = 2; c[1] = c[2] = True; r = 0;
  {1, 2}~Join~Monitor[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--];
        If[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++] ] ];
    If[k > r, r = k; Sow[k]];
    Set[{c[k], j}, {True, k}], {n, 3, nn}] ][[-1, 1]], n] ]

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