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A161962 Odd numbers k such that phi(k) < phi(k+1).

%I A161962 #17 Nov 25 2022 11:17:38
%S A161962 105,165,315,525,585,735,1155,1365,1485,1575,1755,1785,1815,1995,2145,
%T A161962 2205,2415,2475,2535,2805,2835,3003,3045,3315,3465,3675,3885,3927,
%U A161962 4095,4125,4305,4455,4485,4515,4725,4785,4845,4935,5115,5145
%N A161962 Odd numbers k such that phi(k) < phi(k+1).
%C A161962 If k is even then for obvious reasons phi(k) will usually be less than phi(k+1). So it is more interesting to see when this occurs for odd k.
%H A161962 G. C. Greubel, <a href="/A161962/b161962.txt">Table of n, a(n) for n = 1..5000</a>
%F A161962 a(n) = 2*A001836(n) - 1. - _Jon Maiga_ / _Georg Fischer_, Jun 23 2021
%e A161962 105 is in the sequence since phi(105)=48 and phi(106)=52.
%p A161962 with(numtheory): a := proc (n) if `mod`(n, 2) = 1 and phi(n) < phi(n+1) then n else end if end proc: seq(a(n), n = 1 .. 6000); # _Emeric Deutsch_, Jul 11 2009
%t A161962 Select[Range[5500], OddQ[#] && EulerPhi[#] < EulerPhi[# + 1] &] (* _G. C. Greubel_, Feb 27 2019 *)
%t A161962 2#-1&/@Flatten[Position[Partition[EulerPhi[Range[5500]],2],_?(#[[1]]<#[[2]]&),1,Heads-> False]] (* _Harvey P. Dale_, Nov 25 2022 *)
%o A161962 (Sage) [n for n in (1..5500) if mod(n+1,2)==0 and euler_phi(n) < euler_phi(n+1)] # _G. C. Greubel_, Feb 27 2019
%o A161962 (Magma) [n: n in [1..5500] | ((n+1) mod 2 eq 0) and (EulerPhi(n) lt EulerPhi(n+1))]; // _G. C. Greubel_, Feb 27 2019
%o A161962 (PARI) for(n=1, 5500, if(Mod(n+1,2)==0 && eulerphi(n) < eulerphi(n+1), print1(n", "))) \\ _G. C. Greubel_, Feb 27 2019
%Y A161962 Cf. A000010, A001836, A161963.
%K A161962 easy,nonn
%O A161962 1,1
%A A161962 David Angell (angell(AT)maths.unsw.edu.au), Jun 22 2009