A182458 - OEIS

%I #23 May 20 2021 10:56:44

%S 1,2,1,0,1,1,2,3,7,4,9,4,1,5,6,1,7,8,3,6,19,10,15,13,4,3,13,13,2,27,

%T 25,25,18,22,23,17,32,27,29,4,37,26,39,26,3,34,11,46,27,18,37,4,45,22,

%U 19,34,31,29,30,45,31,54,1,55,56,26,5,64,49,32,29,6

%N a(0)=1, a(1)=2, a(n) = (a(n-2)*a(n-1)+1) mod n.

%C Indices of zeros: 3, 284, 295, 1042, 1478, 36382, 52328, 63463, 1564027, 19758967, 152380267, 503372464, 9766438965, 119068745443, 220054053597, 234739914603, 881852361961, 3491882402381, 3681101616539, 5880347601791, 7363426715439, 10328374852578.

%C Conjecture: a(n) contains infinitely many zeros.

%C a(A182472(n)) = n and a(m) <> n for m < A182472(n). [_Reinhard Zumkeller_, May 01 2012]

%H Reinhard Zumkeller, <a href="/A182458/b182458.txt">Table of n, a(n) for n = 0..10000</a>

%t nxt[{n_,a_,b_}]:={n+1,b,Mod[a b+1,n+1]}; Join[{1},Rest[NestList[nxt,{1,2,2},80][[All,2]]]] (* _Harvey P. Dale_, Feb 14 2019 *)

%o (Python)

%o prpr = 1

%o prev = 2

%o for n in range(2,77):

%o     current = ( prev*prpr + 1 ) % n

%o     print(prpr, end=',')

%o     prpr = prev

%o     prev = current

%o (Haskell)

%o a182458 n = a182458_list !! n

%o a182458_list = 1 : 2 : zipWith mod

%o    (map (+ 1) $ zipWith (*) a182458_list (tail a182458_list)) [2..]

%o -- _Reinhard Zumkeller_, May 01 2012

%Y Cf. A182457.

%K nonn,easy

%O 0,2

%A _Alex Ratushnyak_, Apr 30 2012