A007015 - OEIS

A007015

a(n) = smallest k such that phi(n+k) = phi(k).
(Formerly M3212)

1, 4, 3, 8, 5, 24, 5, 13, 9, 20, 7, 48, 13, 16, 13, 26, 17, 52, 19, 37, 21, 44, 13, 96, 25, 34, 27, 32, 13, 124, 17, 52, 33, 41, 19, 104, 35, 52, 37, 65, 25, 123, 17, 73, 39, 92, 41, 183, 35, 76, 39, 68, 53, 156, 35, 64, 57, 116, 41, 248, 61, 73, 61, 104, 65, 144, 67, 82

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

OFFSET

1,2

COMMENTS

Sierpiński proved that a solution exists for each n>0.

REFERENCES

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 840.

R. K. Guy, Unsolved Problems Number Theory, Sect. B36

W. Sierpiński, Sur une propriété de la fonction phi(n), Publ. Math. Debrecen, 4 (1956), 184-185. - Jonathan Sondow, Sep 30 2012

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..10000

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

R. G. Wilson, V, Letter to N. J. A. Sloane, Jul. 1992

MATHEMATICA

kphi[n_]:=Module[{k=1}, While[EulerPhi[n+k]!=EulerPhi[k], k++]; k]; Array[kphi, 70] (* Harvey P. Dale, Oct 24 2011 *)

PROG

(Haskell)

import Data.List (elemIndex)

import Data.Maybe (fromJust)

a007015 n = 1 + (fromJust $

elemIndex 0 $ zipWith (-) a000010_list $ drop n a000010_list)

-- Reinhard Zumkeller, Feb 10 2012

(PARI) a(n)=k=1; while(eulerphi(k)!=eulerphi(n+k), k++); k

vector(100, n, a(n)) \\ Derek Orr, May 05 2015