This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A050473 #18 Nov 05 2024 19:07:03
%S A050473 2,1,1,2,1,4,3,4,3,5,5,8,26,7,5,8,9,12,5,10,7,8,46,16,5,13,9,14,7,25,
%T A050473 21,13,9,17,7,24,62,19,11,20,76,28,13,16,15,23,17,32,21,25,17,26,52,
%U A050473 36,11,28,13,26,13,45,74,28,17,26,13,39,33,31,21,32,13,48,39,37,25,38
%N A050473 Smallest k such that phi(k+n) = 2*phi(k).
%C A050473 Makowski proved that the sequence is well-defined.
%C A050473 It appears that k <= 2n, with equality for the n in A110196 only. Computations for n < 10^6 appear to show that k < n for all but a finite number of n. - _T. D. Noe_, Jul 15 2005
%D A050473 Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B36, p. 138.
%H A050473 Amiram Eldar, <a href="/A050473/b050473.txt">Table of n, a(n) for n = 1..10000</a>
%H A050473 Max Alekseyev, <a href="https://oeis.org/wiki/User:Max_Alekseyev/gpscripts">PARI/GP Scripts for Miscellaneous Math Problems</a> (invphi.gp).
%H A050473 Andrzej Makowski, <a href="https://www.e-periodica.ch/digbib/view?pid=edm-001%3A1974%3A29%3A%3A7#19">On the equation phi(n+k)=2*phi(n)</a>, Elem. Math., Vol. 29, No. 1 (1974), p. 13.
%e A050473 phi(13+26) = 24 = 2*phi(13), so a(13) = 26.
%t A050473 Table[k=1; While[EulerPhi[n+k] != 2*EulerPhi[k], k++ ]; k, {n, 100}] (Noe)
%o A050473 (PARI) f(n) = apply(x -> x - n, select(x -> x > n, invphi(2*eulerphi(n)))); \\ using _Max Alekseyev_'s invphi.gp
%o A050473 lista(len) = {my(v = vector(len), c = 0, k = 1, s); while(c < len, s = f(k); for(i = 1, #s, if(s[i] <= len && v[s[i]] == 0, c++; v[s[i]] = k)); k++); v;} \\ _Amiram Eldar_, Nov 05 2024
%Y A050473 Cf. A000010, A007015, A050472, A110196.
%Y A050473 Cf. A110179 (least k such that phi(n+k)=2*phi(n)).
%K A050473 nonn,look
%O A050473 1,1
%A A050473 _Jud McCranie_, Dec 24 1999