Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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