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First string of 43 consecutive composite numbers.
0

%I #9 Jul 06 2017 04:08:15

%S 15684,15685,15686,15687,15688,15689,15690,15691,15692,15693,15694,

%T 15695,15696,15697,15698,15699,15700,15701,15702,15703,15704,15705,

%U 15706,15707,15708,15709,15710,15711,15712,15713,15714,15715,15716,15717,15718,15719,15720,15721,15722,15723,15724,15725,15726

%N First string of 43 consecutive composite numbers.

%p P:= select(isprime, [seq(i,i=3..20000,2)]):

%p G:= P[2..-1]-P[1..-2]:

%p i0:= ListTools:-SelectFirst(j -> G[j]>=42, [$1..nops(G)]):

%p $ P[i0]+1 .. P[i0]+43; # _Robert Israel_, Jul 05 2017

%t rPrimeNext[n_]:=Module[{k},k=n+1;While[PrimeQ[k]||GCD[n,k]!=1,k++ ];k]; a=1;lst={a};Do[AppendTo[lst,a=rPrimeNext[a]],{n,0,2*7!}];lst1=lst; q=41;lst={};Do[If[lst1[[n+q]]-lst1[[n]]==q,AppendTo[lst,lst1[[n]]]],{n,0,Length[lst1]-q}];lst; a=FromDigits[lst];Table[n,{n,a,a+q}]

%Y Cf. A051884

%K nonn,fini,full

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, May 15 2010

%E Edited by _Robert Israel_, Jul 05 2017