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A259142
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Least prime p of the form n*q^2+(n+1)*r^2 with q and r prime.
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1
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17, 83, 43, 61, 149, 199, 263, 113, 331, 139, 383, 373, 173, 191, 199, 569, 587, 547, 251, 269, 277, 757, 1223, 1321, 859, 347, 787, 373, 3779, 1789, 1063, 953, 433, 1181, 1019, 1069, 1283, 503, 2311, 5209, 1193, 1453, 563, 1301, 2389, 607, 1367, 1657, 641, 659, 1483, 1777, 1811, 1861, 719, 1913, 1657, 1997, 4391, 3229, 797, 1823
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OFFSET
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1,1
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COMMENTS
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Values of {p,q,r}: {17,3,2},{83,2,5},{43,3,2},{61,2,3},{149,5,2},{199,2,5},{263,3,5},{113,2,3}.
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LINKS
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EXAMPLE
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17=1*3^2+2*2^2, 83=2*2^2+3*5^2, 43=3*3^2+4*2^2.
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MAPLE
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P:= [seq(ithprime(i), i=1..20)]: np:= 20:
for n from 1 to 100 do
found:= false;
while not found do
R:= sort([seq(seq(n*q^2+(n+1)*p^2, p=P), q=P)]);
w:= n*4+(n+1)*P[-1]^2+1;
r:= ListTools:-SelectFirst(isprime, R);
if r <> NULL and r <= w then
A[n]:= r;
found:= true;
else
P:= [op(P), seq(ithprime(i), i=np+1..np+20)];
np:= np+20;
fi
od;
od:
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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