

A096451


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.


2



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

1,1


COMMENTS

First term prime(2) = 3 is placed on 0th row.
If prime(n1) = +1 mod 4 is on kth row then we put prime(n) on (k1)st row.
If prime(n1) = 1 mod 4 is on kth 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


LINKS

Robert Israel, Table of n, a(n) for n = 1..811
Andrew Granville and Greg Martin, Prime number races, Amer. Math. Monthly, 113 (No. 1, 2006), 133.


MAPLE

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:
Res; # Robert Israel, Nov 07 2018


CROSSREFS

Cf. A096447A096455.
Cf. A002144, A002145, A007350, A007351
Sequence in context: A319167 A088909 A322388 * A090690 A160026 A141555
Adjacent sequences: A096448 A096449 A096450 * A096452 A096453 A096454


KEYWORD

nonn


AUTHOR

Yasutoshi Kohmoto, Aug 12 2004


EXTENSIONS

More terms from Joshua Zucker, May 03 2006


STATUS

approved



