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A244915
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Smallest positive integer a(n) such that b(n) = a(n)^2 + a(n-1)^2 is a prime different from the primes b(1), b(2), ..., b(n-1), where a(0) = 1.
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2
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1, 1, 2, 3, 8, 5, 2, 7, 8, 13, 2, 15, 4, 1, 6, 5, 4, 9, 10, 1, 14, 9, 16, 1, 20, 3, 10, 7, 12, 13, 10, 17, 2, 27, 10, 19, 6, 11, 4, 21, 10, 29, 4, 25, 6, 29, 16, 5, 18, 7, 20, 11, 14, 15, 22, 5, 24, 1, 26, 5, 28, 13, 20, 19, 14, 25, 12, 17, 8, 23, 12, 43, 8
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OFFSET
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0,3
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COMMENTS
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If every positive integer appears in the sequence infinitely often then the sequence b(n) is a permutation of all primes of the form x^2 + y^2.
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LINKS
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PROG
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(PARI)
a244915(maxn) = {
my(a=[1], b=[], an, bn);
for(n=1, maxn,
an=1;
while(!(isprime(bn=an^2+a[#a]^2) && setsearch(b, bn)==0), an++);
a=concat(a, an);
b=setunion(b, [bn])
);
a
}
(Python)
from sympy import isprime
blist = []
for n in range(1, 100):
....while not isprime(b) or b in blist:
........b += 2*a+1
........a += 1
....blist.append(b)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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