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A096451
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Primes p such that the number of primes less than p equal to 1 mod 4 is two less than the number of primes less than p equal to 3 mod 4.
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2
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13, 29, 37, 53, 61, 71, 79, 101, 107, 113, 131, 139, 151, 163, 199, 359, 409, 421, 433, 443, 457, 479, 1223, 1231, 1249, 1277, 1283, 1291, 1301, 1307, 1399, 1423, 1439, 8699, 8779, 26821, 26951, 26959, 26987, 27011, 27031, 615731, 615869, 615887
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OFFSET
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1,1
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COMMENTS
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First term prime(2) = 3 is placed on 0th row.
If prime(n-1) = +1 mod 4 is on k-th row then we put prime(n) on (k-1)-st row.
If prime(n-1) = -1 mod 4 is on k-th row then we put prime(n) on (k+1)-st row.
This process makes an array of prime numbers:
3, 7, 19, 43, ....0th row
5, 11, 17, 23, 31, 41, 47, 59, 67, 103, 127, ....first row
13, 29, 37, 53, 61, 71, 79, 101, 107, 113 ....2nd row
73, 83, 97, 109, ....3rd row
89, ....4th row
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LINKS
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Andrew Granville and Greg Martin, Prime number races, Amer. Math. Monthly, 113 (No. 1, 2006), 1-33.
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MAPLE
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c1:= 0; c3:= 0: p:= 2: count:= 0: Res:= NULL:
while count < 100 do
p:= nextprime(p);
if c1 = c3 - 2 then
count:= count+1;
Res:= Res, p;
fi;
if p mod 4 = 1 then c1:=c1+1
else c3:= c3+1
fi
od:
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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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