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A241928
a(n) = smallest k such that lambda(n+k) = lambda(k).
1
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, 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, 7, 13, 14, 45, 20, 61, 31, 9, 16, 7, 18, 45, 17, 23, 10, 71, 45, 39
OFFSET
1,2
COMMENTS
Lambda(n) is the Carmichael lambda function(A002322).
It is highly probable that a solution exists for each n>0.
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, ...
LINKS
EXAMPLE
a(29) = 7 because lambda(29+7) = lambda(7) = 6.
MAPLE
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:
MATHEMATICA
klambda[n_]:=Module[{k=1}, While[CarmichaelLambda[n+k]!= CarmichaelLambda [k], k++]; k]; Array[klambda, 70]
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, May 02 2014
STATUS
approved