|
%I M5406 N2349 #31 Feb 04 2022 02:02:01
%S 157,262,367,412,472,487,577,682,787,877,892,907,997,1072,1207,1237,
%T 1312,1402,1522,1567,1627,1657,1732,1852,1942,2047,2062,2152,2194,
%U 2257,2362,2437,2467,2557,2572,2677,2722,2782
%N Numbers k such that phi(2k+1) < phi(2k).
%C Greg Martin (gerg(AT)math.toronto.edu) writes: I recently calculated the smallest solution of phi(30k+1) < phi(30k) (see the Martin link); it has 1116 digits.
%D J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 157, p. 51, Ellipses, Paris 2008.
%D Jeffrey Shallit, personal communication.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Donovan Johnson, <a href="/A001837/b001837.txt">Table of n, a(n) for n = 1..10000</a>
%H V. L. Klee, Jr., <a href="http://www.jstor.org/stable/2305207">Some remarks on Euler's totient function</a>, Amer. Math. Monthly, 54 (1947), 332.
%H Greg Martin, <a href="http://arXiv.org/abs/math/9804025">The smallest solution of phi(30n+1) < phi(30n) is ...</a>, arXiv:math/9804025 [math.NT], 1998; Amer. Math. Monthly, Vol. 106, No. 5 (1999), pp. 449-451.
%H J. Shallit, <a href="/A001274/a001274.pdf">Letter to N. J. A. Sloane, Jul 17 1975</a>
%p with(numtheory,phi); f := proc(n) if phi(2*n+1) < phi(2*n) then RETURN(n) fi end;
%t Select[ Range[4000], EulerPhi[2# + 1] < EulerPhi[2# ] & ]
%o (PARI) isok(n) = eulerphi(2*n+1) < eulerphi(2*n); \\ _Michel Marcus_, Oct 03 2017
%Y Cf. A000010.
%K nonn
%O 1,1
%A _N. J. A. Sloane_
|
