A306877 Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, among the prime divisors of n * a(n) there are at least 4 runs of consecutive prime numbers.

1870, 935, 1729, 1045, 374, 2093, 494, 1235, 2639, 187, 170, 2737, 190, 247, 4301, 1265, 110, 2821, 130, 209, 299, 85, 182, 3367, 418, 95, 3451, 377, 220, 5423, 230, 1495, 391, 55, 598, 3458, 238, 65, 133, 253, 260, 403, 266, 115, 5797, 91, 273, 3689, 741, 319

Offset

1,1

Comments

This sequence is a variant of A285744 and of A306864.

This sequence is a self-inverse permutation of the natural numbers.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..30000

Rémy Sigrist, PARI program for A306877

Index entries for sequences that are permutations of the natural numbers

Formula

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

Example

The first terms, alongside the corresponding runs, are:
  n   a(n)  runs in n*a(n)
  --  ----  --------------
   1  1870  2, 5, 11, 17
   2   935  2, 5, 11, 17
   3  1729  3, 7, 13, 19
   4  1045  2, 5, 11, 19
   5   374  2, 5, 11, 17
   6  2093  2-3, 7, 13, 23
   7   494  2, 7, 13, 19
   8  1235  2, 5, 13, 19
   9  2639  3, 7, 13, 29
  10   187  2, 5, 11, 17
  11   170  2, 5, 11, 17
  12  2737  2-3, 7, 17, 23
  13   190  2, 5, 13, 19
  14   247  2, 7, 13, 19
  15  4301  3-5, 11, 17, 23
  16  1265  2, 5, 11, 23

Prog

(PARI) See Links section.

Crossrefs

Cf. A285744, A287170, A306864.

Sequence in context: A354444 A237152 A306864 * A073495 A073489 A353552

Adjacent sequences: A306874 A306875 A306876 * A306878 A306879 A306880

Keyword

nonn,look

Author

Rémy Sigrist, Mar 14 2019

Status

approved