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a(n)=lcm of first n consecutive prime differences.
6

%I #11 May 13 2017 02:51:45

%S 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 24,24,24,24,168,168,168,168,840,840,840,840,840,840,840,840,840,840,

%U 840,840,840,840,840,840,840,840,840,840,840,840,840,840,840,840,840,840

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

%H Michael De Vlieger, <a href="/A080374/b080374.txt">Table of n, a(n) for n = 1..10000</a>

%e n=25: first 25 distinct differences are {1,2,4,6,8}, lcm=24=a(25)

%e From _Michael De Vlieger_, May 12 2017: (Start)

%e Record values of a(n) set at A080376(n):

%e n A080376(n) a(A080376(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 tb[x_] := Table[Prime[w+1]-Prime[w], {w, 1, x}] Table[Apply[LCM, tb[j]], {j, 1, 256}]

%t (* Second program: *)

%t FoldList[LCM @@ {#1, #2} &, Differences@ Array[Prime, 61]] (* _Michael De Vlieger_, May 12 2017 *)

%o (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 Cf. A001223, A080375.

%K nonn

%O 1,2

%A _Labos Elemer_, Feb 27 2003