A003276 Numbers k such that the multiplicative group of residues prime to k, M_k, is isomorphic to M_{k+1}.
1, 3, 15, 104, 495, 975, 22935, 32864, 57584, 131144, 491535, 2539004, 3988424, 6235215, 7378371, 13258575, 17949434, 25637744, 26879684, 29357475, 32235735, 41246864, 48615735, 184611375, 229944855, 257278724, 290849624, 429461864, 550666515, 671054835, 706075095
Offset: 1
References
- K. Miller, Solutions of phi(n) = phi(n+1) for 1 <= n <= 500000. Unpublished, 1972. [Cf. Math. Comp., Vol. 27, p. 447, 1973.]
- D. Shanks, Solved and Unsolved Problems in Number Theory, 2nd. ed., Chelsea, 1978, p. 225.
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- P. J. Cameron and D. A. Preece, Notes on primitive lambda-roots.
- K. Miller, The equation phi(n) = phi(n+1), Unpublished M.S., ND.
- K. Miller, Solutions of phi(n) = phi(n+1) for 1 <= n <= 500000, Mathematics of Computation 27 (1973), 47-48. (Annotated scanned copy)
Crossrefs
Subsequence of A001274.
Programs
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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 -
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
Extensions
More terms from David W. Wilson