A001837 Numbers k such that phi(2k+1) < phi(2k).

157, 262, 367, 412, 472, 487, 577, 682, 787, 877, 892, 907, 997, 1072, 1207, 1237, 1312, 1402, 1522, 1567, 1627, 1657, 1732, 1852, 1942, 2047, 2062, 2152, 2194, 2257, 2362, 2437, 2467, 2557, 2572, 2677, 2722, 2782

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

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.

References

• J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 157, p. 51, Ellipses, Paris 2008.
• Jeffrey Shallit, personal communication.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Donovan Johnson, Table of n, a(n) for n = 1..10000
• V. L. Klee, Jr., Some remarks on Euler's totient function, Amer. Math. Monthly, 54 (1947), 332.
• Greg Martin, The smallest solution of phi(30n+1) < phi(30n) is ..., arXiv:math/9804025 [math.NT], 1998; Amer. Math. Monthly, Vol. 106, No. 5 (1999), pp. 449-451.
• J. Shallit, Letter to N. J. A. Sloane, Jul 17 1975

Crossrefs

Cf. A000010.

Programs

Maple

with(numtheory,phi); f := proc(n) if phi(2*n+1) < phi(2*n) then RETURN(n) fi end;

Mathematica

Select[ Range[4000], EulerPhi[2# + 1] < EulerPhi[2# ] & ]

PARI

isok(n) = eulerphi(2*n+1) < eulerphi(2*n); \\ Michel Marcus, Oct 03 2017