A182458 a(0)=1, a(1)=2, a(n) = (a(n-2)*a(n-1)+1) mod n.

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, 25, 25, 18, 22, 23, 17, 32, 27, 29, 4, 37, 26, 39, 26, 3, 34, 11, 46, 27, 18, 37, 4, 45, 22, 19, 34, 31, 29, 30, 45, 31, 54, 1, 55, 56, 26, 5, 64, 49, 32, 29, 6

Offset

0,2

Comments

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.

Conjecture: a(n) contains infinitely many zeros.

a(A182472(n)) = n and a(m) <> n for m < A182472(n). [Reinhard Zumkeller, May 01 2012]

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Mathematica

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 *)

Prog

(Python)
prpr = 1
prev = 2
for n in range(2, 77):
    current = ( prev*prpr + 1 ) % n
    print(prpr, end=', ')
    prpr = prev
    prev = current
(Haskell)
a182458 n = a182458_list !! n
a182458_list = 1 : 2 : zipWith mod
   (map (+ 1) $ zipWith (*) a182458_list (tail a182458_list)) [2..]
-- Reinhard Zumkeller, May 01 2012

Crossrefs

Cf. A182457.

Sequence in context: A269941 A035440 A029878 * A238093 A238095 A240608

Adjacent sequences: A182455 A182456 A182457 * A182459 A182460 A182461

Keyword

nonn,easy

Author

Alex Ratushnyak, Apr 30 2012

Status

approved