A093096 Start with a(1) = a(2) = 3; then apply the rule of A093094.

3, 3, 9, 2, 7, 1, 8, 1, 4, 7, 8, 8, 4, 2, 8, 5, 6, 6, 4, 3, 2, 8, 1, 6, 4, 0, 3, 0, 3, 6, 2, 4, 1, 2, 6, 1, 6, 8, 6, 2, 4, 0, 0, 0, 0, 1, 8, 1, 2, 8, 4, 2, 1, 2, 6, 6, 4, 8, 4, 8, 1, 2, 8, 0, 0, 0, 0, 0, 8, 8, 2, 1, 6, 3, 2, 8, 2, 2, 1, 2, 3, 6, 2, 4, 3, 2, 3, 2, 3, 2, 8, 2, 1, 6, 0, 0, 0, 0, 0, 0, 6, 4, 1, 6, 2

Offset: 1

Author

Bodo Zinser, Mar 20 2004

Keywords

• nonn
• base

Comments

Essentially the same as A060310. [From R. J. Mathar, Sep 08 2008]

Examples

			a(3)=a(1)*a(2), a(4)=first digit of (a(2)*a(3)), a(5)=2nd digit of (a(2)*a(3)), a(6)=first digit of (a(3)*a(4)), a(7)=2nd digit of (a(3)*a(4))
		

References

• Hugo Steinhaus, Studentenfutter, Urania, Leipzig 1991, #1.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A045777, A060310, A093094, A093095, A093097, A096381.

Programs

Haskell

a093096 n = a093096_list !! (n-1)
a093096_list = f [3,3] where
   f (u : vs@(v : _)) = u : f (vs ++
     if w < 10 then [w] else uncurry ((. return) . (:)) $ divMod w 10)
        where w = u * v
-- Reinhard Zumkeller, Aug 13 2013

Mathematica

Fold[Join[#, IntegerDigits[Times @@ #[[#2;; #2+1]]]] &, {3, 3}, Range[100]] (* Paolo Xausa, Aug 18 2025 *)

Python

from itertools import islice
from collections import deque
def agen(): # generator of terms
    a = deque([3, 3])
    while True:
        a.extend(list(map(int, str(a[0]*a[1]))))
        yield a.popleft()
print(list(islice(agen(), 105))) # Michael S. Branicky, Aug 18 2025