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%I #18 May 13 2017 23:37:52
%S 2,4,9,24,30,34,99,189,217,282,367,738,3302,3427,3644,3793,4612,7970,
%T 8688,14357,23283,34202,49414,85633,85787,103520,224659,273413,415069,
%U 474029,685903
%N Numbers n where A080374 increases.
%C Numbers where a consecutive prime-difference (prime(a(n)+1)-prime(a(n))) arises with a new prime-power factor.
%e From _Michael De Vlieger_, May 12 2017: (Start)
%e Values of A080374 starting at a(n).
%e n a(n) A080374(a(n))
%e 1 2 1
%e 2 4 2
%e 3 9 4
%e 4 24 12
%e 5 30 24
%e 6 34 168
%e 7 99 840
%e 8 189 2520
%e 9 217 27720
%e 10 282 471240
%e 11 367 942480
%e 12 738 12252240
%e 13 3302 24504480
%e 14 3427 465585120
%e 15 3644 2327925600
%e 16 3793 72165693600
%e 17 4612 216497080800
%e 18 7970 6278415343200
%e 19 8688 144403552893600
%e 20 14357 288807105787200
%e 21 23283 12418705548849600
%e 22 34202 509166927502833600
%e 23 49414 18839176317604843200
%e 24 85633 131874234223233902400
%e 25 85787 6989334413831396827200
%e ...
%e (End)
%t s=1; Do[s1=s; s=LCM[s, Prime[n+1]-Prime[n]]; If[Greater[s, s1], Print[n]], {n, 1, 100000}]
%t (* Second program: *)
%t Most[Accumulate@ #2 + 1] & @@ Transpose@ Map[{First@ #, Length@ #} &, Split@ FoldList[LCM @@ {#1, #2} &, Differences@ Array[Prime, 10^4]]] (* _Michael De Vlieger_, May 12 2017 *)
%Y Cf. A001223, A080374.
%K nonn
%O 1,1
%A _Labos Elemer_, Feb 27 2003
%E Edited by _N. J. A. Sloane_, May 13 2017 at the suggestion of _Michael De Vlieger_.
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