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A139102
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Numbers whose binary representation shows the distribution of prime numbers up to the n-th prime minus 1, using "0" for primes and "1" for nonprime numbers.
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10
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1, 2, 9, 37, 599, 2397, 38359, 153437, 2454999, 157119967, 628479869, 40222711647, 643563386359, 2574253545437, 41188056726999, 2636035630527967, 168706280353789919, 674825121415159677, 43188807770570219359, 691020924329123509751, 2764083697316494039005
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OFFSET
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1,2
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COMMENTS
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a(n) is the decimal representation of A139101(n) interpreted as binary number.
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LINKS
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FORMULA
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EXAMPLE
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a(4)=37 because 37 written in base 2 is 100101 and the string "100101" shows the distribution of prime numbers up to the 4th prime minus 1, using "0" for primes and "1" for nonprime numbers.
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MAPLE
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A139101 := proc(n) option remember ; local a, p; if n = 1 then RETURN(1); else a := 10*A139101(n-1) ; for p from ithprime(n-1)+1 to ithprime(n)-1 do a := 10*a+1 ; od: fi ; RETURN(a) ; end: # R. J. Mathar, Apr 25 2008
bin2dec := proc(n) local nshft ; nshft := convert(n, base, 10) ; add(op(i, nshft)*2^(i-1), i=1..nops(nshft) ) ; end: # R. J. Mathar, Apr 25 2008
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MATHEMATICA
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Table[ sum = 0; For[i = 1, i <= Prime[n] - 1 , i++, sum = sum*2;
If[! PrimeQ[i], sum++]]; sum, {n, 1, 25}] (* Robert Price, Apr 03 2019 *)
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PROG
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(PARI) a(n) = fromdigits(vector(prime(n)-1, k, !isprime(k)), 2); \\ Michel Marcus, Apr 04 2019
(Python)
from sympy import isprime, prime
def a(n):
return int("".join(str(1-isprime(i)) for i in range(1, prime(n))), 2)
(Python) # faster version for initial segment of sequence
from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
an = 0
for k in count(1):
an = 2 * an + int(not isprime(k))
if isprime(k+1):
yield an
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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