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%I #5 May 09 2014 22:51:23
%S 1,4,3,4,3,6,7,4,3,5,5,9,13,7,5,8,17,6,9,4,3,11,23,16,5,13,9,14,7,10,
%T 31,13,9,17,5,36,37,10,13,20,41,14,5,16,15,23,9,36,7,10,17,13,52,9,5,
%U 7,13,14,45,20,61,31,9,16,7,18,45,17,23,10,71,45,39
%N a(n) = smallest k such that lambda(n+k) = lambda(k).
%C Lambda(n) is the Carmichael lambda function(A002322).
%C It is highly probable that a solution exists for each n>0.
%C The corresponding values of lambda(k) are 1, 2, 2, 2, 2, 2, 6, 2, 2, 4, 4, 6, 12, 6, 4, 2, 16, 2, 6, 2, 2, 10, 22, 4, 4, 12, 6, 6, 6, 4, 30, ...
%H Michel Lagneau, <a href="/A241928/b241928.txt">Table of n, a(n) for n = 1..10000</a>
%e a(29) = 7 because lambda(29+7) = lambda(7) = 6.
%p with(numtheory):for n from 1 to 70 do:ii:=0:for k from 1 to 10^8 while(ii=0) do:if lambda(k) = lambda(k+n) then ii:=1:printf(`%d, `,k):else fi:od:od:
%t klambda[n_]:=Module[{k=1}, While[CarmichaelLambda[n+k]!= CarmichaelLambda [k], k++]; k]; Array[klambda, 70]
%Y Cf. A002322, A007015, A173695.
%K nonn
%O 1,2
%A _Michel Lagneau_, May 02 2014
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