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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A054816 A052168 A237152 * A306877 A073495 A073489

Adjacent sequences:  A306861 A306862 A306863 * A306865 A306866 A306867

KEYWORD

nonn,look

AUTHOR

Rémy Sigrist, Mar 14 2019

STATUS

approved

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Last modified January 19 03:54 EST 2020. Contains 331031 sequences. (Running on oeis4.)