A139104 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.

2, 4, 18, 74, 1198, 4794, 76718, 306874, 4909998, 314239934, 1256959738, 80445423294, 1287126772718, 5148507090874, 82376113453998, 5272071261055934, 337412560707579838, 1349650242830319354, 86377615541140438718, 1382041848658247019502, 5528167394632988078010

Offset: 1

Author

Omar E. Pol, Apr 08 2008

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..467
• Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Crossrefs

Subset of A118255.

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

Programs

Mathematica

Table[ sum = 0; For[i = 1, i <= Prime[n] , i++, sum = sum*2;
If[! PrimeQ[i], sum++]]; sum, {n, 1, 21}] (* Robert Price, Apr 03 2019 *)
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 *)

PARI

a(n) = fromdigits(vector(prime(n), k, !isprime(k)), 2); \\ Michel Marcus, Apr 04 2019

Formula

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

From Ridouane Oudra, Aug 27 2019: (Start)

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)

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

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

Extensions

More terms from R. J. Mathar, May 22 2008

a(19)-a(21) from Robert Price, Apr 03 2019