A109853 a(n) = A109852(2^n).

1, 2, 5, 9, 13, 19, 29, 37, 43, 53, 61, 71, 79, 89, 101, 107, 113, 131, 139, 151, 163, 173, 181, 193, 199, 223, 229, 239, 251, 263, 271, 281, 293, 311, 317, 337, 349, 359, 373, 383, 397, 409, 421, 433, 443, 457, 463, 479, 491, 503, 521, 541, 557, 569, 577, 593

Offset: 0

Author

Amarnath Murthy, Jul 07 2005

Keywords

• nonn

Comments

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

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

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

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..1000
• Rémy Sigrist, PARI program for A109853

Crossrefs

Cf. A008578, A031215, A046022, A109852.

Programs

Mathematica

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 *)

PARI

See Links section.

Extensions

More terms from Robert G. Wilson v, Jun 14 2006

More terms from Rémy Sigrist, May 19 2019