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A067843
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Least solution k>n of phi(k-n)+phi(k+n)=phi(2k).
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1
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5, 10, 7, 10, 11, 12, 35, 14, 13, 22, 55, 22, 19, 70, 19, 22, 85, 26, 77, 26, 27, 110, 55, 34, 55, 38, 31, 34, 119, 38, 65, 44, 41, 52, 65, 46, 185, 154, 43, 46, 143, 54, 215, 70, 57, 110, 161, 58, 187, 68, 67, 76, 203, 62, 175, 62, 61, 76, 95, 74, 67, 130, 71, 88, 95, 82, 115, 74, 73, 130, 215
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OFFSET
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1,1
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COMMENTS
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The first n for which a(n)-n is odd is 239.
If n+2 and n+4 are twin primes (i.e. n+2 is in A001359), then a(n) <= n+4.
Conjecture: a(n) >= n+4 for all n. (End)
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LINKS
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EXAMPLE
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k = 10 is the smallest solution of phi(k-2)+phi(k+2)=phi(2k). So a(2) = 10.
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MAPLE
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f:= proc(n) local k;
for k from n+1 do if numtheory:-phi(k-n)+numtheory:-phi(k+n)=numtheory:-phi(2*k) then return k fi od:
end proc:
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MATHEMATICA
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f[k_] := Module[{i = k + 1}, While[EulerPhi[i - k] + EulerPhi[i + k] != EulerPhi[2 i], i++ ]; i]; Table[f[n], {n, 1, 40}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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