A155836 2^(2^n) mod n.

0, 0, 1, 0, 1, 4, 4, 0, 4, 6, 3, 4, 9, 2, 1, 0, 1, 16, 4, 16, 4, 16, 3, 16, 21, 16, 13, 16, 16, 16, 8, 0, 4, 18, 11, 16, 33, 16, 22, 16, 37, 16, 4, 20, 31, 6, 21, 16, 4, 16, 1, 16, 42, 52, 36, 16, 28, 54, 20, 16, 57, 16, 4, 0, 61, 16, 21, 52, 64, 16, 12, 16, 4, 16, 31, 24, 4, 16, 73, 16, 40

Offset

1,6

Comments

From the randomness of the graph, it seems likely that every number will eventually occur. a(n)=1 for the n in A094358. When do 5 and 23 occur? The number 14 finally appears at n=34913. a(n) can be computed rapidly using two applications of the powermod function.

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

Example

a(1941491)=a(43228711)=a(75548489)=5 and a(100867561)=23. See A155886 for the first occurrence of each number. [From T. D. Noe, Jan 31 2009]

Mathematica

Table[e=IntegerExponent[n, 2]; d=n/2^e; k=MultiplicativeOrder[2, d]; r=PowerMod[2, n, k]-e; r=Mod[r, k]; 2^e PowerMod[2, r, d], {n, 100}]
Table[PowerMod[2, 2^n, n], {n, 100}] (* Harvey P. Dale, Oct 16 2022 *)

Prog

(PARI) a(n)=my(ph=eulerphi(n)); lift(Mod(2, n)^(ph+lift(Mod(2, ph)^n))) \\ Charles R Greathouse IV, Feb 24 2012

Crossrefs

A015910 (2^n mod n), A036236.

Sequence in context: A283361 A138518 A290799 * A337398 A245971 A279365

Adjacent sequences: A155833 A155834 A155835 * A155837 A155838 A155839

Keyword

nonn

Author

T. D. Noe, Jan 28 2009

Status

approved