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 #37 Mar 19 2020 14:12:47
%S 1,2,14,1978,38209,4782974,9581014,244330711,365496202,1661392258,
%T 116084432414,288504187458218,490179448388654,802245996685561
%N Positive integers n such that n | (3^n + 5).
%C No other terms below 10^15. Some larger terms: 79854828136468902206, 3518556634988844968631084847788071912030455376274045370172567094578. - _Max Alekseyev_, Oct 14 2016
%e 3^14 + 5 = 4782974 = 14 * 341641, so 14 is a term.
%o (PARI) is(n)=Mod(3,n)^n==-5; \\ _Joerg Arndt_, Oct 09 2016
%o (Python)
%o A277288_list = [1,2]+[n for n in range(3,10**6) if pow(3,n,n)==n-5] # _Chai Wah Wu_, Oct 09 2016
%o (Sage)
%o def A277288_list(search_limit):
%o n, t, r = 1, Integer(3), [1]
%o while n < search_limit:
%o n += 1
%o t *= 3
%o if n.divides(t+5): r.append(n)
%o return r # _Peter Luschny_, Oct 10 2016
%Y Solutions to 3^n == k (mod n): A277340 (k=-11), A277289 (k=-7), this sequence (k=-5), A015973 (k=-2), A015949 (k=-1), A067945 (k=1), A276671 (k=2), A276740 (k=5), A277126 (k=7), A277274 (k=11).
%K nonn,more
%O 1,2
%A _Seiichi Manyama_, Oct 09 2016
%E a(9) from _Joerg Arndt_, Oct 09 2016
%E a(10) from _Chai Wah Wu_, Oct 09 2016
%E a(11)-a(14) from _Max Alekseyev_, Oct 14 2016