A109853 - OEIS

%I #15 May 19 2019 08:53:41

%S 1,2,5,9,13,19,29,37,43,53,61,71,79,89,101,107,113,131,139,151,163,

%T 173,181,193,199,223,229,239,251,263,271,281,293,311,317,337,349,359,

%U 373,383,397,409,421,433,443,457,463,479,491,503,521,541,557,569,577,593

%N a(n) = A109852(2^n).

%C Conjecture: a(n) is prime if n is not 0 nor 2.

%C Conjecture: a(n) is the (2n-2)nd prime for n>1. A109852(2^n-1): 1,3,5,11,17,23,31,41,47,59,67,73. - _Robert G. Wilson v_, Jun 14 2006

%C Conjecture: the Union of A109852(2^n-1) & A109852(2^n) is A046022: {1,2,3,4,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79, ...,} and except for 4, equals A008578: The noncomposite numbers. - _Robert G. Wilson v_, Jun 14 2006

%H Rémy Sigrist, <a href="/A109853/b109853.txt">Table of n, a(n) for n = 0..1000</a>

%H Rémy Sigrist, <a href="/A109853/a109853.gp.txt">PARI program for A109853</a>

%t f[s_] := Block[{k = 2, len = Length@s}, exp = Ceiling[Log[2, len]]; m = s[[2^exp - len + 1]]; While[MemberQ[s, k*m], k++ ]; Append[s, k*m]]; Rest@Nest[f, {1, 1}, 70]; t = Rest@Nest[f, {1, 1}, 2^14 + 3]; Table[t[[2^n]], {n, 0, 14}] (* _Robert G. Wilson v_, Jun 14 2006 *)

%o (PARI) See Links section.

%Y Cf. A008578, A031215, A046022, A109852.

%K nonn

%O 0,2

%A _Amarnath Murthy_, Jul 07 2005

%E More terms from _Robert G. Wilson v_, Jun 14 2006

%E More terms from _Rémy Sigrist_, May 19 2019