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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 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 August 7 23:16 EDT 2022. Contains 355995 sequences. (Running on oeis4.)