cp's OEIS Frontend

A276373 Least k such that phi(k*n-1) = phi(k*n+1), or -1 if no such k exists.

%I A276373 #10 Jun 03 2024 16:04:50
%S A276373 5,4,3,2,1,106,21,1,1,39282,1,53,135,65014,5,9489,171,361,27,19641,7,
%T A276373 13133,141,6326,3,6978,1,32507,375,13094,165,93186,1,1359,9,12588,15,
%U A276373 171,45,35253,3,35794,9,16796,7,1689,69,3163,3,13653,57,3489,12,249,45,58497,9
%N A276373 Least k such that phi(k*n-1) = phi(k*n+1), or -1 if no such k exists.
%C A276373 Least k such that k*n is in A066812.
%C A276373 If n is in A066812 then a(n) = 1, otherwise a(n) = A276052(n).
%H A276373 Jean-François Alcover, <a href="/A276373/b276373.txt">Table of n, a(n) for n = 1..1000</a>
%e A276373 a(5) = 15 because phi(15*5-1) = phi(15*5+1).
%p A276373 f:= proc(n) local k;
%p A276373    for k from 1 do if numtheory:-phi(k*n-1) = numtheory:-phi(k*n+1) then
%p A276373       return k
%p A276373    fi od end proc:
%p A276373 map(f, [$1..60]);
%t A276373 kmax = 10^8;
%t A276373 a[n_] := For[k = 1, k <= kmax, k++, If[EulerPhi[k*n - 1] == EulerPhi[k*n + 1], Print[n, " ", k]; Return[k]]] /. Null -> -1;
%t A276373 Table[a[n], {n, 1, 1000}] (* _Jean-François Alcover_, Jun 03 2024 *)
%Y A276373 Cf. A000010, A066812, A275412, A276052.
%K A276373 nonn
%O A276373 1,1
%A A276373 _Altug Alkan_ and _Robert Israel_, Aug 31 2016