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URL: https://oeis.org/A139104

⇱ A139104 - OEIS

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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.
10
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.
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
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