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Least m such that (prime(n) mod m) > (prime(n+1) mod m).
0

%I #5 May 27 2014 15:18:37

%S 3,4,3,5,3,5,3,5,4,3,4,5,3,5,4,7,3,7,5,3,7,5,4,3,5,3,5,3,5,3,5,4,3,4,

%T 3,4,7,5,4,7,3,7,3,5,3,5,13,5,3,5,7,3,11,4,7,4,3,4,5,3,4,3,5,3,5,3,4,

%U 11,3,5,7,3,4,7,5,4,3,5,3,11,3,11,3,7,5,4,3,5,3,5,7,3,5,3,5,4,5,3,4,7,4,7,4

%N Least m such that (prime(n) mod m) > (prime(n+1) mod m).

%e a(100) = 7 because prime(100) = 541 == 2 mod 7, prime(101) = 547 == 1 mod 7 and 7 is least m such that 541 > 547 mod m.

%t s={};Do[pn=Prime[n];pn1=Prime[n+1];Do[If[Mod[pn,m]>Mod[pn1,m],AppendTo[s,{n,pn,pn1,m}];Break[]],{m,2,200}],{n,1,130}];Last/@s

%t lm[n_]:=Module[{m=2,pn0=Prime[n],pn1=Prime[n+1]},While[Mod[pn0,m]<= Mod[ pn1,m],m++];m]; Array[lm,110] (* _Harvey P. Dale_, May 27 2014 *)

%K nonn

%O 1,1

%A _Zak Seidov_, Aug 31 2006