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A118255 a(1)=1, then a(n)=2*a(n-1) if n is prime, a(n)=2*a(n-1)+1 if n not prime. 8
1, 2, 4, 9, 18, 37, 74, 149, 299, 599, 1198, 2397, 4794, 9589, 19179, 38359, 76718, 153437, 306874, 613749, 1227499, 2454999, 4909998, 9819997, 19639995, 39279991, 78559983, 157119967, 314239934, 628479869, 1256959738, 2513919477, 5027838955, 10055677911 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

In base 2 a(n) is the concatenation for i=1 to n of A005171(i).

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = floor(k * 2^n) where k = 0.585317... = 1 - A051006. [Charles R Greathouse IV, Dec 27 2011]

EXAMPLE

a(2) = 2*1 = 2 as 2 is prime;

a(3) = 2*2 = 4 as 3 is prime;

a(4) = 2*4+1 = 9 as 4 is composite;

a(5) = 2*9 = 18 as 5 is prime.

MAPLE

f:=proc(n) option remember; if n=1 then RETURN(1); fi; if isprime(n) then 2*f(n-1) else 2*f(n-1)+1; fi; end; # N. J. A. Sloane

MATHEMATICA

nxt[{n_, a_}]:={n+1, If[PrimeQ[n+1], 2a, 2a+1]}; Transpose[NestList[nxt, {1, 1}, 40]][[2]] (* Harvey P. Dale, Jan 22 2015 *)

Array[FromDigits[#, 2] &@ Array[Boole[! PrimeQ@ #] &, #] &, 34] (* Michael De Vlieger, Nov 01 2016 *)

CROSSREFS

Cf. A005171, A051006, A118256, A118257.

Sequence in context: A152537 A182028 A081253 * A206927 A019299 A052932

Adjacent sequences:  A118252 A118253 A118254 * A118256 A118257 A118258

KEYWORD

nonn

AUTHOR

Pierre CAMI, Apr 19 2006

EXTENSIONS

Corrected by Omar E. Pol, Nov 08 2007

Corrections verified by N. J. A. Sloane, Nov 17 2007

STATUS

approved

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Last modified April 23 09:35 EDT 2019. Contains 322385 sequences. (Running on oeis4.)