A001837 Numbers k such that phi(2k+1) < phi(2k). (Formerly M5406 N2349)

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

1,1

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

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# ] & ]

Prog

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

Crossrefs

Cf. A000010.

Sequence in context: A216498 A275317 A303094 * A142581 A140625 A142874

Adjacent sequences: A001834 A001835 A001836 * A001838 A001839 A001840

Keyword

nonn

Author

N. J. A. Sloane

Status

approved