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A080376 Numbers n where A080374 increases. 5
2, 4, 9, 24, 30, 34, 99, 189, 217, 282, 367, 738, 3302, 3427, 3644, 3793, 4612, 7970, 8688, 14357, 23283, 34202, 49414, 85633, 85787, 103520, 224659, 273413, 415069, 474029, 685903 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers where a consecutive prime-difference (prime(a(n)+1)-prime(a(n))) arises with a new prime-power factor.

LINKS

Table of n, a(n) for n=1..31.

EXAMPLE

From Michael De Vlieger, May 12 2017: (Start)

Values of A080374 starting at a(n).

    n     a(n)   A080374(a(n))

    1       2    1

    2       4    2

    3       9    4

    4      24    12

    5      30    24

    6      34    168

    7      99    840

    8     189    2520

    9     217    27720

   10     282    471240

   11     367    942480

   12     738    12252240

   13    3302    24504480

   14    3427    465585120

   15    3644    2327925600

   16    3793    72165693600

   17    4612    216497080800

   18    7970    6278415343200

   19    8688    144403552893600

   20   14357    288807105787200

   21   23283    12418705548849600

   22   34202    509166927502833600

   23   49414    18839176317604843200

   24   85633    131874234223233902400

   25   85787    6989334413831396827200

...

(End)

MATHEMATICA

s=1; Do[s1=s; s=LCM[s, Prime[n+1]-Prime[n]]; If[Greater[s, s1], Print[n]], {n, 1, 100000}]

(* Second program: *)

Most[Accumulate@ #2 + 1] & @@ Transpose@ Map[{First@ #, Length@ #} &, Split@ FoldList[LCM @@ {#1, #2} &, Differences@ Array[Prime, 10^4]]] (* Michael De Vlieger, May 12 2017 *)

CROSSREFS

Cf. A001223, A080374.

Sequence in context: A326908 A229048 A144309 * A005669 A038664 A261367

Adjacent sequences:  A080373 A080374 A080375 * A080377 A080378 A080379

KEYWORD

nonn

AUTHOR

Labos Elemer, Feb 27 2003

EXTENSIONS

Edited by N. J. A. Sloane, May 13 2017 at the suggestion of Michael De Vlieger.

STATUS

approved

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Last modified January 26 11:23 EST 2020. Contains 331279 sequences. (Running on oeis4.)