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A003276

Numbers k such that the multiplicative group of residues prime to k, M_k, is isomorphic to M_{k+1}.
(Formerly M3000)

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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 Unpublished, 1972.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

Table of n, a(n) for n=1..31.

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K. Miller, The equation phi(n) = phi(n+1), Unpublished M.S., ND.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)

PROG

(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

CROSSREFS

Subsequence of A001274.

Sequence in context: A331689 A001274 A139766 * A136092 A338724 A273197

Adjacent sequences: A003273 A003274 A003275 * A003277 A003278 A003279

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from David W. Wilson

STATUS

approved