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

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

Crossrefs

Cf. A000010.

Sequence in context: A022998 A082895 A086938 * A354139 A114562 A189042

Adjacent sequences: A007012 A007013 A007014 * A007016 A007017 A007018

Keyword

nonn,nice

Author

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

Extensions

More terms from Jud McCranie, Dec 24 1999

Status

approved