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

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

Offset: 1

Author

N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v

Keywords

• nonn
• nice

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

Crossrefs

Cf. A000010.

Programs

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

Mathematica

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

PARI

a(n)=k=1;while(eulerphi(k)!=eulerphi(n+k),k++);k
vector(100,n,a(n)) \\ Derek Orr, May 05 2015

Extensions

More terms from Jud McCranie, Dec 24 1999