A306864 Lexicographically earliest sequence of distinct positive terms such that among the prime divisors of the product of two consecutive terms there are at least 4 runs of consecutive prime numbers.

1, 1870, 2, 935, 4, 1045, 8, 1235, 10, 187, 20, 209, 40, 247, 14, 299, 21, 377, 28, 391, 22, 85, 44, 95, 26, 115, 34, 55, 38, 65, 46, 91, 57, 182, 19, 110, 17, 220, 23, 130, 29, 170, 11, 190, 13, 230, 31, 238, 37, 260, 41, 266, 39, 133, 52, 145, 68, 155, 76

Offset

1,2

Comments

This sequence is a variant of A285487.

This sequence is likely a permutation of the natural numbers.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..25000

Rémy Sigrist, Scatterplot of the first 25000 terms

Rémy Sigrist, PARI program for A306864

Formula

A287170(a(n) * a(n+1)) >= 4.

Example

The first terms, alongside the corresponding runs, are:
   n   a(n)  runs in a(n)*a(n+1)
  ---  ----  -------------------
    1     1  2, 5, 11, 17
    2  1870  2, 5, 11, 17
    3     2  2, 5, 11, 17
    4   935  2, 5, 11, 17
    5     4  2, 5, 11, 19
    6  1045  2, 5, 11, 19
    7     8  2, 5, 13, 19
    8  1235  2, 5, 13, 19
    9    10  2, 5, 11, 17
   10   187  2, 5, 11, 17
   11    20  2, 5, 11, 19
   12   209  2, 5, 11, 19
  ...
   32    91  3, 7, 13, 19
   33    57  2-3, 7, 13, 19
   34   182  2, 7, 13, 19
  ...
  662  1222  2, 7, 13, 47
  663   448  2, 7, 17, 73
  664  1241  2-3, 7-11, 17, 73
  665   462  2-3, 7-11, 29, 43
  666  1247  3, 17, 29, 43
  ...

Prog

(PARI) See Links section.

Crossrefs

Cf. A287170, A285487.

Sequence in context: A052168 A354444 A237152 * A306877 A073495 A073489

Adjacent sequences: A306861 A306862 A306863 * A306865 A306866 A306867

Keyword

nonn,look

Author

Rémy Sigrist, Mar 14 2019

Status

approved