A001836 Numbers k such that phi(2k-1) < phi(2k), where phi is Euler's totient function A000010.

53, 83, 158, 263, 293, 368, 578, 683, 743, 788, 878, 893, 908, 998, 1073, 1103, 1208, 1238, 1268, 1403, 1418, 1502, 1523, 1658, 1733, 1838, 1943, 1964, 2048, 2063, 2153, 2228, 2243, 2258, 2363, 2393, 2423, 2468, 2558, 2573, 2633, 2657, 2678

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice

References

• 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

• T. D. Noe, Table of n, a(n) for n = 1..1000
• V. L. Klee, Jr., Some remarks on Euler's totient function, Amer. Math. Monthly, 54 (1947), 332.
• Don Reble, Python program.
• J. Shallit, Letter to N. J. A. Sloane, Jul 17 1975.

Crossrefs

Cf. A000010, A001837.

Programs

Haskell

a001836 n = a001836_list !! (n-1)
a001836_list = f a000010_list 1 where
   f (u:v:ws) x = if u < v then x : f ws (x + 1) else f ws (x + 1)
-- Reinhard Zumkeller, Jul 11 2014

Maple

with(numtheory): A001836:=n->`if`(phi(2*n-1) < phi(2*n), n, NULL): seq(A001836(n), n=1..5*10^3); # Wesley Ivan Hurt, Oct 10 2014

Mathematica

Select[Range[3000], EulerPhi[2# - 1] < EulerPhi[2#] &] (* Harvey P. Dale, Apr 01 2012 *)
Position[Partition[EulerPhi[Range[6000]],2],?(#[[1]]<#[[2]]&),1,Heads-> False]//Flatten (* _Harvey P. Dale, Jul 02 2021 *)

PARI

is(n)=eulerphi(2*n-1)Charles R Greathouse IV, Feb 21 2013

Python

from sympy import totient
def ok(n): return totient(2*n - 1) < totient(2*n) # Indranil Ghosh, Apr 29 2017

Extensions

Corrected and extended by Don Reble, Jan 04 2007