A139104 - OEIS

%I #24 Aug 28 2019 09:53:59

%S 2,4,18,74,1198,4794,76718,306874,4909998,314239934,1256959738,

%T 80445423294,1287126772718,5148507090874,82376113453998,

%U 5272071261055934,337412560707579838,1349650242830319354,86377615541140438718,1382041848658247019502,5528167394632988078010

%N Numbers whose binary representation shows the distribution of prime numbers up to the n-th prime, using "0" for primes and "1" for nonprime numbers.

%C a(n) is the decimal representation of A139103(n) interpreted as binary number.

%H Harvey P. Dale, <a href="/A139104/b139104.txt">Table of n, a(n) for n = 1..467</a>

%H Omar E. Pol, <a href="http://polprimos.com">Determinacion geometrica de los numeros primos y perfectos</a>.

%F a(n) = 2 * A139102(n).

%F From _Ridouane Oudra_, Aug 27 2019: (Start)

%F a(n) = 2^prime(n) - 1 - (1/2)*(n + Sum_{i=1..prime(n)} 2^(prime(n)-i)*pi(i)), where prime(n) = A000040(n) and pi(n) = A000720(n)

%F a(n) = A001348(n) - A121240(n)

%F a(n) = A118255(A000040(n)). (End)

%e a(4)=74 because 74 written in base 2 is 1001010 and the string "1001010" shows the distribution of prime numbers up to the 4th prime, using "0" for primes and "1" for nonprime numbers.

%t Table[ sum = 0; For[i = 1, i <= Prime[n] , i++, sum = sum*2;

%t If[! PrimeQ[i], sum++]]; sum, {n, 1, 21}] (* _Robert Price_, Apr 03 2019 *)

%t Module[{nn=30,t},t=Table[If[PrimeQ[n],0,1],{n,Prime[nn]}];Table[ FromDigits[ Take[t,p],2],{p,Prime[Range[nn]]}]] (* _Harvey P. Dale_, Jul 15 2019 *)

%o (PARI) a(n) = fromdigits(vector(prime(n), k, !isprime(k)), 2); \\ _Michel Marcus_, Apr 04 2019

%Y Subset of A118255.

%Y Cf. A000040, A018252, A139101, A139102, A139103, A139119, A139120, A139122, A000720, A001348, A121240.

%K nonn

%O 1,1

%A _Omar E. Pol_, Apr 08 2008

%E More terms from _R. J. Mathar_, May 22 2008

%E a(19)-a(21) from _Robert Price_, Apr 03 2019