



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
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OFFSET

0,2


COMMENTS

Conjecture: a(n) is prime if n is not 0 nor 2.
Conjecture: a(n) is the (2n2)nd prime for n>1. A109852(2^n1): 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^n1) & 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



