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A302442
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Number of primes of the form b^2-2 for b <= 10^n.
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3
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OFFSET
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1,1
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COMMENTS
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Table C(i) = a(i)/pi(10^i) = a(i)/A000720(10^i)
a(1) = 5 C(1) = 1.25000000
a(2) = 26 C(2) = 1.04000000
a(3) = 157 C(3) = 0.93452381
a(4) = 1153 C(4) = 0.93816111
a(5) = 8888 C(5) = 0.92660550
a(6) = 72928 C(6) = 0.92904278
a(7) = 615643 C(7) = 0.92636541
a(8) = 5328644 C(8) = 0.92487818
a(9) = 47034083 C(9) = 0.92500224
a(10) = 420950239 C(10) = 0.92505860
(End)
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LINKS
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EXAMPLE
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a(1) = 5 because there are 5 primes of the form b^2-2 for b <= 10 : 2, 7, 23, 47 and 79.
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PROG
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(PARI) {a(n) = sum(k=0, 10^n, isprime(k^2-2))}
(Python)
from sympy import isprime
def aupton(terms):
s, alst = 0, []
for n in range(1, terms+1):
s += sum(isprime(b**2-2) for b in range(10**(n-1), 10**n))
alst.append(s)
return alst
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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