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A007015 a(n) = smallest k such that phi(n+k) = phi(k).
(Formerly M3212)
27

%I M3212

%S 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,

%T 34,27,32,13,124,17,52,33,41,19,104,35,52,37,65,25,123,17,73,39,92,41,

%U 183,35,76,39,68,53,156,35,64,57,116,41,248,61,73,61,104,65,144,67,82

%N a(n) = smallest k such that phi(n+k) = phi(k).

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

%D 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.

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

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

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A007015/b007015.txt">Table of n, a(n) for n=1..10000</a>

%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

%H R. G. Wilson, V, <a href="/A007015/a007015.pdf">Letter to N. J. A. Sloane, Jul. 1992</a>

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

%o (Haskell)

%o import Data.List (elemIndex)

%o import Data.Maybe (fromJust)

%o a007015 n = 1 + (fromJust $

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

%o -- _Reinhard Zumkeller_, Feb 10 2012

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

%o vector(100,n,a(n)) \\ _Derek Orr_, May 05 2015

%Y Cf. A000010.

%K nonn,nice

%O 1,2

%A _N. J. A. Sloane_, _Mira Bernstein_, _Robert G. Wilson v_

%E More terms from _Jud McCranie_, Dec 24 1999

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Last modified March 26 10:18 EDT 2019. Contains 321491 sequences. (Running on oeis4.)