A248219 Indices where A248218(n) = 1.

1, 3, 7, 19, 21, 31, 37, 43, 57, 93, 111, 129, 133, 157, 217, 259, 301, 307, 313, 399, 463, 471, 499, 589, 613, 651, 703, 777, 817, 903, 921, 939, 967, 1099, 1147, 1333, 1389, 1497, 1591, 1767, 1839, 2109, 2149, 2191, 2451, 2683, 2901, 2983, 3241, 3297, 3441

Offset

1,2

Comments

n is in the sequence if there exists a number k0 such that A003095(k) mod n = A003095(k0) mod n for all k >= k0.

Conjecture: a(n) ~ n^2.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..717

Example

7 is in the sequence since A003095 mod 7 is {1, 2, 5, 5, 5, 5, ...}, k0 = 3, A003095(k) mod 7 = 5 for all k >= k0. The period is 1.
10 is not in the sequence since A003095 mod 10 is {1, 2, 5, 6, 7, 0, 1, 2, 5, 6, 7, 0, 1, 2, ...} and the period is 6, not 1.

Mathematica

nmax=10000; periods=Table[m=Rest[NestList[Mod[#^2+1, n]&, 0, nmax]]; period=0; j=1; While[j<=Length[m]&&period==0, If[m[[Length[m]-j]]==m[[Length[m]]], period=j]; j++]; period, {n, 1, nmax}]; Select[Range[nmax], periods[[#]]==1&]

Crossrefs

Cf. A003095, A247981, A248218.

Sequence in context: A089749 A032667 A109991 * A322963 A018432 A205302

Adjacent sequences: A248216 A248217 A248218 * A248220 A248221 A248222

Keyword

nonn

Author

Vaclav Kotesovec, Oct 04 2014

Status

approved