A182457 a(0)=0, a(1)=1, a(n) = (a(n-2)*a(n-1)+1) mod n.

0, 1, 1, 2, 3, 2, 1, 3, 4, 4, 7, 7, 2, 2, 5, 11, 8, 4, 15, 4, 1, 5, 6, 8, 1, 9, 10, 10, 17, 26, 23, 10, 7, 5, 2, 11, 23, 32, 15, 13, 36, 18, 19, 42, 7, 25, 38, 11, 35, 43, 6, 4, 25, 48, 13, 20, 37, 0, 1, 1, 2, 3, 7, 22, 27, 10, 7, 4, 29, 48, 63, 43, 46, 8

Offset

0,4

Comments

Indices of zeros:

0, 57, 123, 1975, 2551, 5473, 5537, 7271, 39480, 132993, 153539, 224581, 5925390, 10243877, 123259126, 284753964, 2520364708, 2985427716, 5115049972, 11066575675, 13451039887, 33557189081, 242574973569, 5212220671625, 10346718074797

Conjecture: a(n) contains infinitely many zeros.

Links

Ivan Neretin, Table of n, a(n) for n = 0..10000

Mathematica

Nest[Append[#, Mod[#[[-1]]*#[[-2]] + 1, Length[#] + 1]] &, {1, 1}, 71] (* Ivan Neretin, May 14 2015 *)

Prog

(Python)
prpr = 0
prev = 1
for n in range(2, 77):
.  current = ( prev*prpr + 1 ) % n
.  print prpr,
.  prpr = prev
.  prev = current

Crossrefs

Cf. A182458.

Sequence in context: A037222 A107357 A251718 * A368605 A334715 A026105

Adjacent sequences: A182454 A182455 A182456 * A182458 A182459 A182460

Keyword

nonn,easy

Author

Alex Ratushnyak, Apr 30 2012

Status

approved