%I #33 Aug 08 2021 22:04:50
%S 1,5,55,355,605,3905,6655,25205,42955,73205,201995,277255,472505,
%T 805255,1789555,2221945,3049805,5197555,5693105,6049555,7321105,
%U 8857805,14341645,19685105,24441395,28150705,33547855,57173105,62624155,66545105,80532155,97435855,114935155,127058405
%N Numbers k that divide s(k), where s(1)=1, s(j)=5*s(j-1)+j.
%C The sequence so far (for k > 1) is the smallest terms of the values of (5 * 11^i * 71^m) for i,m >= 0. Is there another term (prime?) in the product or can it be proved that all terms have this form?
%o (PARI) lista(nn) = {nb = 1000; for (n=1, nn, v = vector(nb, i, (5^(i+(n-1)*nb+1)-4*(i+(n-1)*nb)-5)/(16*(i+(n-1)*nb))); w = select(n->(type(n) == "t_INT"), v, 1); for (k=1, #w, print1(w[k]+(n-1)*nb, ", ")); kill(v););} \\ _Michel Marcus_, May 31 2014
%o (PARI) is(n) = n%2 == 1 && lift(Mod(5, n)^(n + 1) - Mod(5, n)) == 0 \\ _David A. Corneth_, Aug 08 2021
%Y s(n) = A014827(n).
%K nonn
%O 1,2
%A _N. J. A. Sloane_, _Olivier GĂ©rard_
%E Comment and more terms from Larry Reeves (larryr(AT)acm.org), Mar 24 2000
%E a(10)-a(13) from _Michel Marcus_, May 31 2014
%E a(14)-a(17) from _Jinyuan Wang_, Aug 08 2021
%E a(18)-a(21) from _Michael S. Branicky_, Aug 08 2021
%E a(22)-a(34) from _David A. Corneth_, Aug 08 2021