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A179186
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Numbers n such that phi(n) = phi(n+4), with Euler's totient function phi=A000010.
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12
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8, 14, 16, 20, 35, 52, 64, 91, 140, 148, 244, 292, 403, 455, 616, 628, 772, 801, 1011, 1024, 1108, 1144, 1252, 1270, 1295, 1456, 1588, 1684, 1820, 1828, 2030, 2164, 2452, 2623, 2644, 2660, 2692, 2932, 3028, 3216, 3321, 3508, 3988, 4264, 4340, 4372, 4612, 4804, 4852, 4948
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OFFSET
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1,1
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COMMENTS
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Is there some n > 5 such that phi(n) = phi(n+3)?
No further solutions to the phi(n) = phi(n+3) problem less than 10^12. On the other hand, this sequence has 267797240 terms under 10^12. - Jud McCranie, Feb 13 2012
No reason is known that would prevent other solutions of phi(n)=phi(n+3), see Graham, Holt, & Pomerance. - Jud McCranie, Jan 03 2013
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REFERENCES
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S. W. Graham, J. J. Holt, & C. Pomerance, "On the solutions to phi(n)=phi(n+k)", Number Theory in Progress, Proc. Intern. Conf. in Honor of 60th Birthday of A. Schinzel, Poland, 1997. Walter de Gruyter, 1999, pp. 867-82.
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LINKS
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MATHEMATICA
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Select[Range[5000], EulerPhi[#]==EulerPhi[#+4]&] (* Harvey P. Dale, Feb 16 2011 *)
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PROG
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(PARI) {op=vector(N=4); for( n=1, 1e4, if( op[n%N+1]+0==op[n%N+1]=eulerphi(n), print1(n-N, ", ")))}
(Magma) [n: n in [1..5000] | EulerPhi(n) eq EulerPhi(n+4)]; // Vincenzo Librandi, Sep 08 2016
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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