A386482 -id:A386482 - cp's OEIS frontend

A387072 Index of n in A386482, or -1 if n does not appear in A386482.

1, 2, 5, 3, 17, 4, 11, 9, 6, 8, 24, 7, 44, 10, 16, 14, 52, 13, 31, 15, 12, 23, 73, 22, 18, 21, 26, 20, 126, 19, 57, 29, 25, 28, 41, 27, 115, 30, 43, 40, 809, 39, 821, 38, 42, 37, 76, 36, 49, 35, 51, 34, 652, 33, 70, 48, 32, 47, 144, 46, 189, 56, 50, 55, 45, 54

Offset: 1

Michael De Vlieger, Aug 15 2025

Michael De Vlieger, Table of n, a(n) for n = 1..20000

Cf. A386482.

Block[{a, j, k, p, m, s, nn},
  nn = 2^10; a[] := 0; m[] := 1; a[1] = 1; j = a[2] = 2;
  Monitor[Do[
    If[PrimePowerQ[j],
      Set[{p, k, m}, {#1, #1^(#2 - 1), #1^(#2 - 1)}] & @@
        FactorInteger[j][[1]]; While[And[a[k*p] != 0, k != 0], k--];
        If[k == 0, k = m; While[a[k*p] != 0, k++] ]; k *= p,
      k = j - 1; While[And[Or[a[k] != 0, CoprimeQ[j, k]], k != 1], k--];
      If[k == 1, k += j; While[Or[a[k] != 0, CoprimeQ[j, k] ], k++] ] ];
    Set[{a[k], j}, {n, k}], {n, 3, nn}], n];
  k = 1; Reap[While[a[k] > 0, Sow[a[k]]; k++] ][[-1, 1]] ]

A386487 A386482(n) - n.

Original entry on oeis.org

0, 0, 1, 2, -2, 3, 5, 2, -1, 4, -4, 9, 5, 2, 5, -1, -12, 7, 11, 8, 5, 2, -1, -13, 8, 1, 9, 6, 3, 8, -12, 25, 21, 18, 15, 12, 9, 6, 3, 0, -6, 3, -4, -31, 20, 14, 11, 8, 0, 13, 0, -35, 15, 12, 9, 6, -26, 35, 31, 28, 25, 22, 19, 16, 13, 10, 7, 4, 1, -15, 4, -3, -50, 18, 19, -29, 64, 60, 57, 54, 51, 48, 45, 42, 39, 36, 33, 30, 27, 24, 21

Offset: 1

N. J. A. Sloane, Sep 01 2025

N. J. A. Sloane, Table of n, a(n) for n = 1..10000

Cf. A386482.

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

Michael De Vlieger, Aug 15 2025

Michael De Vlieger, Table of n, a(n) for n = 1..4310 (all primes that appear within the first 2^24 terms of A386462.)
Michael De Vlieger, Log log scatterplot of a(n) n = 1..4310.

Cf. A386482, A387077.

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] ]

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

Michael De Vlieger, Aug 15 2025

Michael De Vlieger, Table of n, a(n) for n = 1..4310

Cf. A386482, A387076.

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] ]

A386483 Index of n-th prime in A386482, or -1 if that prime is missing.

Original entry on oeis.org

2, 5, 17, 11, 24, 44, 52, 31, 73, 126, 57, 115, 809, 821, 76, 652, 144, 189, 667, 674, 678, 207, 287, 1016, 832, 2020, 320, 310, 2026, 2637, 368, 236, 453, 996, 1206, 3017, 3541, 3544, 4876, 1425, 1497, 2425, 2053, 2747, 3006, 4867, 684, 12680, 12803, 12808, 12898, 12901, 6247, 12907, 13279, 837, 2442, 2445, 9513, 9795, 13080, 13088

Offset: 1

N. J. A. Sloane, Aug 16 2025

nonn

Rémy Sigrist, Table of n, a(n) for n = 1..2500
Rémy Sigrist, PARI program

Cf. A386482, A387072, A387076, A387077.

PARI
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\\ See Links section.
```

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

Michael De Vlieger, Aug 15 2025

Michael De Vlieger, Table of n, a(n) for n = 1..140

Cf. A386462, A387074.

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] ]

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

Michael De Vlieger, Aug 15 2025

Michael De Vlieger, Table of n, a(n) for n = 1..140

Cf. A386482, A387073.

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] ]

A386484 a(n) is the index where A387090(n) appears in A386482.

Original entry on oeis.org

1, 2, 5, 17, 24, 44, 52, 73, 126, 809, 821, 1016, 2020, 2026, 2637, 3017, 3541, 3544, 4876, 12680, 12803, 12808, 12898, 12901, 12907, 13279, 17729, 17734, 27224, 33351, 35295, 35310, 44605, 44609, 44925, 44930, 44935, 44939, 45176, 45279, 45703, 45723, 46125, 46138, 46154, 46157, 62957, 63713, 63720, 63869, 63872, 63877, 115110, 115116

Offset: 1

N. J. A. Sloane, Aug 16 2025

A387090 lists the numbers that are the slowest to appear in A386482, and the present sequence tells when they do appear. This is of interest because we do not know if every number appears in A386482.

Rémy Sigrist, Table of n, a(n) for n = 1..1243 (first 127 terms from N. J. A. Sloane)
Rémy Sigrist, C++ program

Cf. A386482, A386483, A387072, A387090.

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

Michael De Vlieger, Aug 15 2025

sign

Michael De Vlieger, Table of n, a(n) for n = 1..10000
Michael De Vlieger, Logarithmic scatterplot of log_10 |a(n)|, n = 1..2^20, showing negative values in red and positive in green.

Cf. A386482.

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] ]

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

Michael De Vlieger, Aug 15 2025

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.
Singleton parity: S(1) = 1 (given), S(125) = 150, and S(13312) = 15776. No further singletons for n < 17150000. These are occasions where S(n) is the largest even number v in S(1..n), further, S(m) = v-2 is the last record high even number only surpassed by v, and there has been at least 1 odd term between S(n) and the last even number before it.

			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.

Michael De Vlieger, Table of n, a(n) for n = 1..260 (run lengths available given 17125588 terms of S).
Michael De Vlieger, Log log scatterplot of a(n), n = 1..260, accentuating run lengths of even terms in red.

Cf. A386482.

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] ]

cp's OEIS Frontend

A387072 Index of n in A386482, or -1 if n does not appear in A386482.

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A386487 A386482(n) - n.

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

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A387077 Indices of prime terms in A386482.

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A386483 Index of n-th prime in A386482, or -1 if that prime is missing.

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PARI

A387073 Record high points in A386482.

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A387074 Indices of record high points in A386482.

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A386484 a(n) is the index where A387090(n) appears in A386482.

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A387075 First differences of A386482.

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

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