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A330251 Numbers k such that phi(k) = phi(k+3), where phi (A000010) is Euler's totient function.

%I A330251 #28 Mar 01 2020 10:07:20
%S A330251 3,5,8720288051472,9134280520365,41544070492925,42466684755492,
%T A330251 51363581614342,68616494581632,113312918293575,210911076210835,
%U A330251 215517565688425,294988451482725,383617980270525,432759876053505,442863123838135,532068058516992,892813363927485,923102743748185,929531173876305
%N A330251 Numbers k such that phi(k) = phi(k+3), where phi (A000010) is Euler's totient function.
%C A330251 10^15 < a(20) <= 1089641067389872.
%C A330251 Also terms: 1248817919303952, 1332436545865422, 1394926716616125, 1868522795664525, 1950445682260072.
%C A330251 a(4) and a(9) appear in Kevin Ford's paper.
%H A330251 Kevin Ford, <a href="https://arxiv.org/abs/2002.12155">Solutions of phi(n)=phi(n+k) and sigma(n)=sigma(n+k)</a>, arXiv:2002.12155 [math.NT], 2020.
%H A330251 S. W. Graham, J. J. Holt, and C. Pomerance, <a href="https://math.dartmouth.edu/~carlp/phi.pdf">On the solutions to phi(n) = phi(n+k)</a>, Number Theory in Progress, K. Gyory, H. Iwaniec, and J. Urbanowicz, eds., vol. 2, de Gruyter, Berlin and New York, 1999, pp. 867-882.
%H A330251 Mathematics StackExchange, <a href="https://math.stackexchange.com/questions/3369378/conjecture-on-the-gap-between-integers-having-the-same-number-of-co-primes/3369432">Conjecture on the gap between integers having the same number of co-primes</a>, Sep 25 2019.
%t A330251 Select[Range[100000], EulerPhi[#] == EulerPhi[# + 3] &] (* _Alonso del Arte_, Mar 01 2020 *)
%o A330251 (PARI) isok(k) = eulerphi(k) == eulerphi(k+3); \\ _Michel Marcus_, Feb 29 2020
%Y A330251 Cf. A000010, A007015.
%Y A330251 Cf. A001274, A001494, A179186, A179187, A179188, A179189, A179202, A330429.
%Y A330251 Cf. A276503, A276504, A217139.
%K A330251 nonn
%O A330251 1,1
%A A330251 _Michel Marcus_ and _Giovanni Resta_, Feb 29 2020