A067843 Least solution k>n of phi(k-n)+phi(k+n)=phi(2k).

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

Offset: 1

Author

Joseph L. Pe, Feb 11 2002

Keywords

• nonn

Comments

From Robert Israel, Jun 08 2018: (Start)

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)

Examples

			k = 10 is the smallest solution of phi(k-2)+phi(k+2)=phi(2k). So a(2) = 10.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A067701.

Programs

Maple

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:
map(f, [$1..100]); # Robert Israel, Jun 08 2018

Mathematica

f[k_] := Module[{i = k + 1}, While[EulerPhi[i - k] + EulerPhi[i + k] != EulerPhi[2 i], i++ ]; i]; Table[f[n], {n, 1, 40}]

Extensions

More terms from Robert Israel, Jun 08 2018