A014852 Numbers k that divide s(k), where s(1)=1, s(j)=5*s(j-1)+j.

1, 5, 55, 355, 605, 3905, 6655, 25205, 42955, 73205, 201995, 277255, 472505, 805255, 1789555, 2221945, 3049805, 5197555, 5693105, 6049555, 7321105, 8857805, 14341645, 19685105, 24441395, 28150705, 33547855, 57173105, 62624155, 66545105, 80532155, 97435855, 114935155, 127058405

Offset: 1

Author

N. J. A. Sloane, Olivier Gérard

Keywords

• nonn

Comments

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?

Crossrefs

s(n) = A014827(n).

Programs

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

PARI

is(n) = n%2 == 1 && lift(Mod(5, n)^(n + 1) - Mod(5, n)) == 0 \\ David A. Corneth, Aug 08 2021

Extensions

Comment and more terms from Larry Reeves (larryr(AT)acm.org), Mar 24 2000

a(10)-a(13) from Michel Marcus, May 31 2014

a(14)-a(17) from Jinyuan Wang, Aug 08 2021

a(18)-a(21) from Michael S. Branicky, Aug 08 2021

a(22)-a(34) from David A. Corneth, Aug 08 2021