This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A167767 #23 Sep 02 2025 14:35:04 %S A167767 1,2,7,8,20,31,32,33,146,211,314,384,626,674,1754,2694,2695,5186, %T A167767 11714,12242,17329,17613,19310,25544,35774,36728,38018,40227,42626, %U A167767 56834,65731,91106,97724,110971,117536,131071,131072,155821,161734,164174 %N A167767 First of 3 or more consecutive integers with equal values of phi(phi(n)). %C A167767 Let p2(n) = phi(phi(n)). This list shows numbers n such that p2(n) = p2(n+1) = p2(n+2) = x for some x. %C A167767 Here phi is Euler's totient function. %H A167767 Donovan Johnson, <a href="/A167767/b167767.txt">Table of n, a(n) for n = 1..500</a> %F A167767 {n: A010554(n) = A010554(n+1) = A010554(n+2)}. - _R. J. Mathar_, Nov 12 2009 %e A167767 p2(1) = p2(2) = p2(3) = 1, p2(7) = p2(8) = p2(9) = 2. %t A167767 Select[Range[100], EulerPhi[EulerPhi[#]] == EulerPhi[EulerPhi[# + 1]] && EulerPhi[EulerPhi[#]] == EulerPhi[EulerPhi[# + 2]] &] (* _G. C. Greubel_, Jun 23 2016 *) %t A167767 SequencePosition[EulerPhi[EulerPhi[Range[170000]]],{x_,x_,x_}][[;;, 1]] (* _Harvey P. Dale_, Sep 02 2025 *) %o A167767 (PARI) isok(n) = (eulerphi(eulerphi(n)) == eulerphi(eulerphi(n+1))) && (eulerphi(eulerphi(n)) == eulerphi(eulerphi(n+2))) \\ _Michel Marcus_, Jul 12 2013 %o A167767 (Magma) [n: n in [1..2*10^5] | EulerPhi(EulerPhi(n)) eq EulerPhi(EulerPhi(n + 1)) and EulerPhi(EulerPhi(n)) eq EulerPhi(EulerPhi(n + 2))]; // _Vincenzo Librandi_, Jun 24 2016 %Y A167767 Cf. A167768. %K A167767 nonn,changed %O A167767 1,2 %A A167767 _Fred Schneider_, Nov 11 2009 %E A167767 Edited by _N. J. A. Sloane_, Nov 12 2009 %E A167767 Extended by _R. J. Mathar_, Nov 12 2009