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A079545
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Primes of the form x^2 + y^2 + 1 with x,y >= 0.
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6
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2, 3, 5, 11, 17, 19, 37, 41, 53, 59, 73, 83, 101, 107, 131, 137, 149, 163, 179, 181, 197, 227, 233, 251, 257, 293, 307, 347, 389, 401, 443, 467, 491, 521, 523, 563, 577, 587, 593, 613, 641, 677, 739, 773, 809, 811, 821, 883
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Bredihin proved that this sequence was infinite. Motohashi improved the upper and lower bounds. [Charles R Greathouse IV, Sep 16 2011]
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REFERENCES
| Y. Motohashi, "On the distribution of prime numbers which are of the form x^2 + y^2 + 1. II". Acta Mathematica Academiae Scientiarum Hungaricae 22 (1971), pp. 207-210.
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LINKS
| Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
B. M. Bredihin, Binary additive problems of indeterminate type II. Analogue of the problem of Hardy and Littlewood (in Russian). Izvestiya Akademii Nauk SSSR Seriya Matematicheskaya 27 (1963), pp. 577-612.
Y. Motohashi, On the distribution of prime numbers which are of the form x^2 + y^2 + 1. Acta Arithmetica 16 (1969), pp. 351-364.
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EXAMPLE
| 17 = 0^2 + 4^2 + 1 is prime so in this sequence.
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PROG
| (PARI) list(lim)={
my(A, t, v=List([2]));
forstep(a=2, sqrt(lim-1), 2,
A=a^2+1;
forstep(b=0, min(a, sqrt(lim-A)), 2,
if(isprime(t=A+b^2), listput(v, t))
)
);
forstep(a=1, sqrt(lim-2), 2,
A=a^2+1;
forstep(b=1, min(a, sqrt(lim-A)), 2,
if(isprime(t=A+b^2), listput(v, t))
)
);
vecsort(Vec(v), , 8)
}; \\ Charles R Greathouse IV, Sep 16 2011
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CROSSREFS
| Cf. A079544, A079739, A079740.
Sequence in context: A040083 A045308 A147813 * A154755 A040095 A040028
Adjacent sequences: A079542 A079543 A079544 * A079546 A079547 A079548
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jan 23 2003
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