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

Author

Rémy Sigrist, Mar 14 2019

Keywords

• nonn
• look

Comments

This sequence is a variant of A285487.

This sequence is likely a permutation of the natural numbers.

Examples

			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
  ...
		

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

Crossrefs

Cf. A287170, A285487.

Programs

PARI

See Links section.

Formula

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