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%I M3000 #36 Nov 29 2023 17:03:27
%S 1,3,15,104,495,975,22935,32864,57584,131144,491535,2539004,3988424,
%T 6235215,7378371,13258575,17949434,25637744,26879684,29357475,
%U 32235735,41246864,48615735,184611375,229944855,257278724,290849624,429461864,550666515,671054835,706075095
%N Numbers k such that the multiplicative group of residues prime to k, M_k, is isomorphic to M_{k+1}.
%D K. Miller, Solutions of phi(n) = phi(n+1) for 1 <= n <= 500000. Unpublished, 1972. [Cf. Math. Comp., Vol. 27, p. 447, 1973.]
%D D. Shanks, Solved and Unsolved Problems in Number Theory, 2nd. ed., Chelsea, 1978, p. 225.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H P. J. Cameron and D. A. Preece, <a href="http://www.maths.qmul.ac.uk/~pjc/csgnotes/lambda.pdf">Notes on primitive lambda-roots</a>.
%H K. Miller, <a href="/A003275/a003275.pdf">The equation phi(n) = phi(n+1)</a>, Unpublished M.S., ND.
%H K. Miller, <a href="/A003275/a003275_1.pdf">Solutions of phi(n) = phi(n+1) for 1 <= n <= 500000</a>, Mathematics of Computation 27 (1973), 47-48. (Annotated scanned copy)
%o (PARI) {my(z=znstar(1));for(n=1,10^10,my(z1=znstar(n+1)); if(z[1]==z1[1]&&z[2]==z1[2],print1(n,", "));z=z1;); } \\ _Joerg Arndt_, Mar 17 2016
%o (PARI) list(lim)=my(v=List(),old=[1,[]]); forfactored(n=2,lim\1+1, my(cur=znstar(n)[1..2]); if(old==cur, listput(v,n[1]-1)); old=cur); Vec(v) \\ _Charles R Greathouse IV_, Jul 17 2022
%Y Subsequence of A001274.
%K nonn,nice
%O 1,2
%A _N. J. A. Sloane_
%E More terms from _David W. Wilson_
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