%I #17 Apr 10 2020 22:10:13
%S 1,2,4,44,82,236,25433,177764,219244,86150213,107218402,1260236441,
%T 12856300141,447650116364,657175627369,14543842704596,125035120614917
%N Positive integers n such that 13^n == 5 (mod n).
%C No other terms below 10^15.
%C Some larger terms: 99790373907467602, 846248577183963835642742, 273781047810302314432122404459324, 4174626353309446327489382394518975030641698849116, 211*(13^211-5)/12607932861823674049268705845744 (207 digits). - _Max Alekseyev_, Jun 29 2011
%e 44 is in this sequence because 13^44 = 10315908977942302627204470186314316211062255002161 = 234452476771415968800101595143507186615051250049*44 + 5 == 5 (mod 44).
%t Join[{1, 2}, Select[Range[1000000], PowerMod[13, #, #] == 5 &]] (* _Robert Price_, Apr 10 2020 *)
%o (PARI) is(n) = Mod(13,n)^n==5; \\ _Charles R Greathouse IV_, Jun 08 2015
%Y Solutions to 13^n == k (mod n): A001022 (k=0), A015963 (k=-1), A116621 (k=1), A116622 (k=2), A116629 (k=3), A116630 (k=4), this sequence (k=5), A116631 (k=6), A116632 (k=7), A295532 (k=8), A116636 (k=9), A116620(k=10), A116638 (k=11), A116639 (k=15).
%Y Cf. A116609, A128121, A276740, A123091.
%K nonn
%O 1,2
%A _Zak Seidov_, Feb 19 2006
%E More terms from _Ryan Propper_, Apr 01 2006
%E Terms 1,2,4 are prepended and a(13)-a(17) are added by _Max Alekseyev_, Jun 29 2011, Nov 27 2017