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

1,1

Comments

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

Links

Harvey P. Dale, Table of n, a(n) for n = 1..467

Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

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)

Example

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.

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 *)

Prog

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

Crossrefs

Subset of A118255.

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

Sequence in context: A174085 A325850 A052689 * A014448 A277033 A295767

Adjacent sequences: A139101 A139102 A139103 * A139105 A139106 A139107

Keyword

nonn

Author

Omar E. Pol, Apr 08 2008

Extensions

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

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

Status

approved