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

0,2

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

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 *)

Prog

(PARI) See Links section.

Crossrefs

Cf. A008578, A031215, A046022, A109852.

Sequence in context: A120615 A038707 A290140 * A071705 A281171 A190713

Adjacent sequences: A109850 A109851 A109852 * A109854 A109855 A109856

Keyword

nonn

Author

Amarnath Murthy, Jul 07 2005

Extensions

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

More terms from Rémy Sigrist, May 19 2019

Status

approved