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A080374 a(n)=lcm of first n consecutive prime differences.

%I A080374 #11 May 13 2017 02:51:45
%S A080374 1,2,2,4,4,4,4,4,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,24,24,
%T A080374 24,24,24,24,168,168,168,168,840,840,840,840,840,840,840,840,840,840,
%U A080374 840,840,840,840,840,840,840,840,840,840,840,840,840,840,840,840,840,840
%N A080374 a(n)=lcm of first n consecutive prime differences.
%H A080374 Michael De Vlieger, <a href="/A080374/b080374.txt">Table of n, a(n) for n = 1..10000</a>
%e A080374 n=25: first 25 distinct differences are {1,2,4,6,8}, lcm=24=a(25)
%e A080374 From _Michael De Vlieger_, May 12 2017: (Start)
%e A080374 Record values of a(n) set at A080376(n):
%e A080374     n  A080376(n)  a(A080376(n))
%e A080374     1        2     1
%e A080374     2        4     2
%e A080374     3        9     4
%e A080374     4       24     12
%e A080374     5       30     24
%e A080374     6       34     168
%e A080374     7       99     840
%e A080374     8      189     2520
%e A080374     9      217     27720
%e A080374    10      282     471240
%e A080374    11      367     942480
%e A080374    12      738     12252240
%e A080374    13     3302     24504480
%e A080374    14     3427     465585120
%e A080374    15     3644     2327925600
%e A080374    16     3793     72165693600
%e A080374    17     4612     216497080800
%e A080374    18     7970     6278415343200
%e A080374    19     8688     144403552893600
%e A080374    20    14357     288807105787200
%e A080374    21    23283     12418705548849600
%e A080374    22    34202     509166927502833600
%e A080374    23    49414     18839176317604843200
%e A080374    24    85633     131874234223233902400
%e A080374    25    85787     6989334413831396827200
%e A080374   ...
%e A080374 (End)
%t A080374 tb[x_] := Table[Prime[w+1]-Prime[w], {w, 1, x}] Table[Apply[LCM, tb[j]], {j, 1, 256}]
%t A080374 (* Second program: *)
%t A080374 FoldList[LCM @@ {#1, #2} &, Differences@ Array[Prime, 61]] (* _Michael De Vlieger_, May 12 2017 *)
%o A080374 (PARI) lista(nn) = {my(v = primes(nn)); my(vd = vector(nn-1, i, v[i+1] - v[i])); for (i=1, nn-1, print1(lcm(vector(i, k, vd[k])), ", "););} \\ _Michel Marcus_, May 13 2017
%Y A080374 Cf. A001223, A080375.
%K A080374 nonn
%O A080374 1,2
%A A080374 _Labos Elemer_, Feb 27 2003