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%I #45 Oct 08 2018 18:14:06
%S 1,4700063497,3468371109448915,8365386194032363,10991007971508067
%N Numbers n such that 2^n == 3 (mod n).
%C No other terms below 10^18. - _Max Alekseyev_, Oct 17 2017
%C Terms were computed: a(2) by the Lehmers, a(3) by _Max Alekseyev_, a(4) and a(5) by Joe K. Crump, a(?) = 63130707451134435989380140059866138830623361447484274774099906755 by P.-L. Montgomery.
%D R. Daniel Mauldin and S. M. Ulam, Mathematical problems and games. Adv. in Appl. Math. 8 (1987), pp. 281-344.
%H Joe K. Crump, <a href="http://web.archive.org/web/20120104074313/http://www.immortaltheory.com/NumberTheory/2nmodn.htm">2^n mod n</a>
%H R. K. Guy, <a href="https://www.maa.org/sites/default/files/pdf/upload_library/22/Ford/Guy697-712.pdf">The Strong Law of Small Numbers</a>, Amer. Math. Monthly 95 (1988), pp. 697-712. See example 13.
%H R. K. Guy, <a href="/A005165/a005165.pdf">The strong law of small numbers</a>. Amer. Math. Monthly 95 (1988), no. 8, 697-712. [Annotated scanned copy]
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/2.html">2</a>
%H OEIS Wiki, <a href="/wiki/2^n mod n">2^n mod n</a>
%t m = 2; Join[Select[Range[m], Divisible[2^# - m, #] &],
%t Select[Range[m + 1, 10^6], PowerMod[2, #, #] == m &]] (* _Robert Price_, Oct 08 2018 *)
%o (PARI) is(n)=Mod(2,n)^n==3 \\ _Charles R Greathouse IV_, Jun 11 2015
%Y Cf. A001567, A036236, A015940, A015910.
%K nonn,more,hard
%O 1,2
%A _Eric W. Weisstein_
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