login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A001494 Numbers n such that phi(n) = phi(n+2).
(Formerly M3293 N1328)
17
4, 7, 8, 10, 26, 32, 70, 74, 122, 146, 308, 314, 386, 512, 554, 572, 626, 635, 728, 794, 842, 910, 914, 1015, 1082, 1226, 1322, 1330, 1346, 1466, 1514, 1608, 1754, 1994, 2132, 2170, 2186, 2306, 2402, 2426, 2474, 2590, 2642, 2695, 2762, 2906, 3242, 3314 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If p and 2p-1 are odd primes then 2(2p-1) is a solution of the equation. Other terms (7,8,32,70,...) are not of this form.

There are 506764111 terms under 10^12. - Jud McCranie, Feb 13 2012

A000010(a(n)) = A000010(a(n) + 2). - Reinhard Zumkeller, Feb 08 2013

REFERENCES

D. M. Burton, Elementary Number Theory, section 7-2.

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

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

LINKS

T. D. Noe and Jud McCranie, Table of n, a(n) for n = 1..10000 (T. D. Noe supplied 1000 terms)

Kevin Ford, Solutions of phi(n)=phi(n+k) and sigma(n)=sigma(n+k), arXiv:2002.12155 [math.NT], 2020.

M. F. Hasler, Table of n, a(n) for n = 1..17286. (Terms up to 10^7.)

V. L. Klee, Jr., Some remarks on Euler's totient function, Amer. Math. Monthly, 54 (1947), 332.

Leo Moser, Some equations involving Euler's totient function, Amer. Math. Monthly, 56 (1949), 22-23.

MAPLE

with(numtheory): P:=proc(n) if phi(n)=phi(n+2) then n;

fi; end: seq(P(i), i=1..3400); # Paolo P. Lava, Mar 02 2018

MATHEMATICA

Select[Range[3500], EulerPhi[#]==EulerPhi[#+2]&] (* Harvey P. Dale, Apr 24 2011 *)

Flatten[Position[Partition[EulerPhi[Range[3500]], 3, 1], _?(#[[1]]==#[[3]]&), {1}, Heads->False]] (* This program is more efficient than the first program above because it only has to calculate phi of each number once. *) (* Harvey P. Dale, Aug 20 2014 *)

PROG

(PARI) op=[0, c=0]; for( n=1, 1e7, if( op[bittest(n, 0)+1]+0==op[bittest(n, 0)+1]=eulerphi(n), write("b001494.txt", c++, " "n-2))) \\ M. F. Hasler, Jan 05 2011

(Haskell)

import Data.List (elemIndices)

a001494 n = a001494_list !! (n-1)

a001494_list = map (+ 1) $ elemIndices 0 $

               zipWith (-) (drop 2 a000010_list) a000010_list

-- Reinhard Zumkeller, Feb 08 2013

(MAGMA) [n: n in [1..4000] | EulerPhi(n) eq EulerPhi(n+2)]; // Vincenzo Librandi, Sep 07 2016

CROSSREFS

Cf. A000010, A001274, A007015, A179186, A179187, A179188, A179189, A179202, A217139.

Sequence in context: A084791 A310933 A186712 * A092214 A319926 A128373

Adjacent sequences:  A001491 A001492 A001493 * A001495 A001496 A001497

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Jud McCranie, Dec 24 1999

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 12 12:20 EDT 2020. Contains 336439 sequences. (Running on oeis4.)