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Smallest positive even number in the sequence (k+1)^n (mod k^n) for k=1,2,3....
1

%I #7 Mar 30 2012 18:52:14

%S 10,46,52,15406,450066,117116,225159022,1872426,680627620,223657336,

%T 147298,589192,11922706,74527876206,141991475986,2377827762166,

%U 584200732,32196037719226,4698165844,18792663376,2948912018446566,175158375580,700633502320,708490569714927006,2737249942690

%N Smallest positive even number in the sequence (k+1)^n (mod k^n) for k=1,2,3....

%C The corresponding value of k is in A188889.

%e a(3)=10 because (k+1)^3 = 10 (mod k^3) for k=3 but no smaller k.

%e a(4)=46 because (k+1)^4 = 46 (mod k^4) for k=5 but no smaller k.

%t Table[k=1; While[r=Mod[(k+1)^n,k^n]; r==0 || OddQ[r], k++]; r, {n,3,30}]

%K nonn

%O 3,1

%A _Vladimir Joseph Stephan Orlovsky_, Apr 08 2011