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%I M3212 #51 Dec 22 2021 00:04:26
%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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