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%I A173695 #24 May 30 2023 02:21:56
%S A173695 1,3,15,90,104,495,665,702,740,836,975,1628,2625,2834,2849,3800,7384,
%T A173695 12402,12560,13050,15250,16470,22935,25928,26274,29574,29890,32864,
%U A173695 39524,41451,44286,47519,48326,48704,48872,49050,50850,53130,54816,56790,56864,57584,63456
%N A173695 Numbers k such that lambda(k) = lambda(k+1).
%C A173695 Lambda(n) is the Carmichael lambda function (A002322).
%C A173695 For k>3 in the sequence, k and k+1 are both composite. - _Robert Israel_, Oct 31 2016
%C A173695 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 A173695 Amiram Eldar, <a href="/A173695/b173695.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..372 from Robert Israel)
%e A173695 104 is in the sequence because lambda(104) = lambda(105) = 12.
%p A173695 with(numtheory):for n from 1 to 50000 do:if lambda(n)=lambda(n+1)then printf(`%d,
%p A173695   `, n):else fi:od:
%t A173695 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 A173695 SequencePosition[CarmichaelLambda[Range[64000]],{x_,x_}][[;;,1]] (* _Harvey P. Dale_, Feb 22 2023 *)
%o A173695 (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 A173695 Cf. A002322.
%K A173695 nonn
%O A173695 1,2
%A A173695 _Michel Lagneau_, Nov 25 2010

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