# [seqfan] A001576

vincenzo.librandi at tin.it vincenzo.librandi at tin.it
Tue Feb 10 17:40:26 CET 2009

```Conjecture
If a(n) =1^n+2^n+4^n= prime number,
then
n is the
form
3^h.

Example:
For h=1, n=3, and 1^3+2^3+4^3=73 (prime)

h=2, n=9,
and
1^9+2^9+4^9=262657 (prime)
Regards,
Vincenzo
Librandi

%I A001576
%S A001576
3,7,21,73,273,1057,4161,16513,65793,262657,1049601,4196353,16781313,
%T
A001576
67117057,268451841,1073774593,4295032833,17180000257,68719738881,
%U
A001576 274878431233,1099512676353,4398048608257,17592190238721
%N
A001576 1^n + 2^n + 4^n.
%C A001576 Equals A135576, except the first
member. [From Omar E. Pol (info(AT)polprimos.com),
Nov
18
2008]
%F A001576 a(n) = 6*a(n-1) - 8*a(n-2) +3.
%F A001576 O.g.f.: -1
/
(-1+x)-1/(-1+2*x)-1/(-1+4*x). - R. J. Mathar (mathar(AT)strw.
leidenuniv.nl),
Feb 29 2008
%F A001576 E.g.f.: e^x+e^
(2*x)+e^(4*x) [From Mohammad K. Azarian (azarian(AT)evansville.edu),
Dec 26 2008]
%t A001576 Table[1^n + 2^n + 4^n, {n, 0,
24}]
%Y A001576 Cf. A001550, A034513, A001579, A074501 - A074580.
%Y
A001576 Cf. A135576, A135577. [From Omar E. Pol (info(AT)polprimos.
com), Nov
18 2008]
%Y A001576 Sequence in context:
A148678 A148679 A148680 this_sequence A075211 A075212

A049365
%Y
A001576 Adjacent sequences: A001573 A001574 A001575
this_sequence
A001577 A001578
A001579
%K A001576 easy,
nonn
%O A001576
0,1
%A A001576 njas

```