%I #24 May 30 2023 02:21:56

%S 1,3,15,90,104,495,665,702,740,836,975,1628,2625,2834,2849,3800,7384,

%T 12402,12560,13050,15250,16470,22935,25928,26274,29574,29890,32864,

%U 39524,41451,44286,47519,48326,48704,48872,49050,50850,53130,54816,56790,56864,57584,63456

%N Numbers k such that lambda(k) = lambda(k+1).

%C Lambda(n) is the Carmichael lambda function (A002322).

%C For k>3 in the sequence, k and k+1 are both composite. - _Robert Israel_, Oct 31 2016

%C Numbers k such that lambda(k) = lambda(k+1) = lambda(k+2) are 16274635445, 42107181364, and no more below 1.6*10^11. - _Amiram Eldar_, May 30 2023

%H Amiram Eldar, <a href="/A173695/b173695.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..372 from Robert Israel)

%e 104 is in the sequence because lambda(104) = lambda(105) = 12.

%p with(numtheory):for n from 1 to 50000 do:if lambda(n)=lambda(n+1)then printf(`%d,

%p `, n):else fi:od:

%t seq[kmax_] := Module[{s = {}, c1 = 0, c2}, Do[c2 = CarmichaelLambda[k]; If[c1 == c2, AppendTo[s, k - 1]]; c1 = c2, {k, 1, kmax}]; s]; seq[10^5] (* _Amiram Eldar_, Feb 22 2023 *)

%t SequencePosition[CarmichaelLambda[Range[64000]],{x_,x_}][[;;,1]] (* _Harvey P. Dale_, Feb 22 2023 *)

%o (PARI) lista(kmax) = {my(c1 = 0, c2); for(k = 1, kmax, c2 = lcm(znstar(k)[2]); if(c1 == c2, print1(k-1,", ")); c1 = c2);} \\ _Amiram Eldar_, Feb 22 2023

%Y Cf. A002322.

%K nonn

%O 1,2

%A _Michel Lagneau_, Nov 25 2010