A276052 Least k > 1 such that phi(k*n-1) = phi(k*n+1), or -1 if no such k exists.

5, 4, 3, 2, 15, 106, 21, 127, 3, 39282, 3, 53, 135, 65014, 5, 9489, 171, 361, 27, 19641, 7, 13133, 141, 6326, 3, 6978, 19, 32507, 375, 13094, 165, 93186, 19, 1359, 9, 12588, 15, 171, 45, 35253, 3, 35794, 9, 16796, 7, 1689, 69, 3163, 3, 13653, 57, 3489, 12, 249, 45, 58497, 9

Offset: 1

Author

Altug Alkan, Aug 17 2016

Keywords

• nonn

Comments

Least k > 1 such that k*n is in A066812. - Robert Israel, Aug 30 2016

Examples

			a(5) = 15 because phi(15*5-1) = phi(15*5+1).
		

Crossrefs

Cf. A000010, A066812, A275412.

Programs

Maple

f:= proc(n) local k;
   for k from 2 do if numtheory:-phi(k*n-1) = numtheory:-phi(k*n+1) then
      return k
   fi od end proc:
map(f, [$1..60]); # Robert Israel, Aug 30 2016

Mathematica

kmax = 10^9;
a[n_] := Module[{k}, For[k = 2, k <= kmax, k++, If[EulerPhi[k n - 1] == EulerPhi[k n + 1] , Print[n, " ", k]; Return[k]]]; -1];
Array[a, 60] (* Jean-François Alcover, Oct 06 2020 *)

PARI

a(n) = {my(k = 2); while (eulerphi(k*n+1) != eulerphi(k*n-1), k++); k; }

Extensions

Name corrected by Robert Israel, Aug 30 2016