OFFSET

1,3

COMMENTS

3 divides a(2k+1) for k>0. Corresponding primes of the form (k^2*2^n + 1) are listed in A122912[n] = {3,5,73,17,1153,257,1153,257,18433,25601,18433,65537,1179649,65537,1179649,65537,1179649,26214401,117964801,...}. There are repeating patterns in a(n) such that for many n a(n) = 2*a(n+2) and a(n+1) = 2*a(n+3). For example, {6,2,3,1}, {12,2,6,1}, {42,18,21,9}, {96,40,48,20,24,10,12,5,6}, {66,10,33,5}, {48,80,24,40,12,20,6,10,3}, {366,38,183,19}. These patterns correspond to identical twin runs in A122912[n] such that A122912[n] = A122912[n+2] and A122912[n+1] = A122912[n+3]. The final index of many such twin runs is perfect power such as {8,16,25,64,81,100,...}.

FORMULA

a(n) = Sqrt[ (A122912[n] - 1) / 2^n ].

CROSSREFS

KEYWORD

nonn

AUTHOR

Alexander Adamchuk, Sep 18 2006

STATUS

approved