A212844 a(n) = 2^(n+2) mod n.

0, 0, 2, 0, 3, 4, 1, 0, 5, 6, 8, 4, 8, 2, 2, 0, 8, 4, 8, 4, 11, 16, 8, 16, 3, 16, 23, 8, 8, 16, 8, 0, 32, 16, 2, 4, 8, 16, 32, 24, 8, 4, 8, 20, 23, 16, 8, 16, 22, 46, 32, 12, 8, 4, 7, 16, 32, 16, 8, 4, 8, 16, 32, 0, 63, 58, 8, 64, 32, 36, 8, 40, 8, 16, 47

Offset

1,3

Comments

Also a(n) = x^x mod (x-2), where x = n+2.

Indices of 0's: 2^k, k>=0.

Indices of 1's: 7, 511, 713, 11023, 15553, 43873, 81079, 95263, 323593, 628153, 2275183, 6520633, 6955513, 7947583, 10817233, 12627943, 14223823, 15346303, 19852423, 27923663, 28529473, ...

Conjecture: every integer k >= 0 appears in a(n) at least once.

Each number below 69 appears at least once. Some large first occurrences: a(39806401) = 25, a(259274569) = 33, a(10571927) = 55, a(18039353) = 81. - Charles R Greathouse IV, Jul 21 2015

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

a(n) = 2^(n+2) mod n.

Example

a(3) = 2^5 mod 3 = 32 mod 3 = 2.

Maple

A212844 := proc(n)
    modp( 2&^ (n+2), n) ;
end proc: # R. J. Mathar, Jul 24 2012

Mathematica

Table[PowerMod[2, n+2, n], {n, 79}] (* Alonso del Arte, Jul 22 2012 *)

Prog

(Python)
for n in range(1, 99):
    print(2**(n+2) % n, end=', ')
(PARI) A212844(n)=lift(Mod(2, n)^(n+2)) \\ M. F. Hasler, Jul 23 2012

Crossrefs

Cf. A000312, A015910, A062173, A112983, A213381, A213859.

Sequence in context: A307320 A350227 A137372 * A066439 A352579 A241319

Adjacent sequences: A212841 A212842 A212843 * A212845 A212846 A212847

Keyword

nonn

Author

Alex Ratushnyak, Jul 22 2012

Status

approved