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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.

%I A096451 #16 Nov 08 2018 08:53:52
%S A096451 13,29,37,53,61,71,79,101,107,113,131,139,151,163,199,359,409,421,433,
%T A096451 443,457,479,1223,1231,1249,1277,1283,1291,1301,1307,1399,1423,1439,
%U A096451 8699,8779,26821,26951,26959,26987,27011,27031,615731,615869,615887
%N 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.
%C A096451 First term prime(2) = 3 is placed on 0th row.
%C A096451 If prime(n-1) = +1 mod 4 is on k-th row then we put prime(n) on (k-1)-st row.
%C A096451 If prime(n-1) = -1 mod 4 is on k-th row then we put prime(n) on (k+1)-st row.
%C A096451 This process makes an array of prime numbers:
%C A096451 3, 7, 19, 43, ....0th row
%C A096451 5, 11, 17, 23, 31, 41, 47, 59, 67, 103, 127, ....first row
%C A096451 13, 29, 37, 53, 61, 71, 79, 101, 107, 113 ....2nd row
%C A096451 73, 83, 97, 109, ....3rd row
%C A096451 89, ....4th row
%H A096451 Robert Israel, <a href="/A096451/b096451.txt">Table of n, a(n) for n = 1..811</a>
%H A096451 Andrew Granville and Greg Martin, <a href="http://www.jstor.org/stable/27641834">Prime number races</a>, Amer. Math. Monthly, 113 (No. 1, 2006), 1-33.
%p A096451 c1:= 0; c3:= 0: p:= 2: count:= 0: Res:= NULL:
%p A096451 while count < 100 do
%p A096451   p:= nextprime(p);
%p A096451   if c1 = c3 - 2 then
%p A096451     count:= count+1;
%p A096451     Res:= Res, p;
%p A096451   fi;
%p A096451   if p mod 4 = 1 then c1:=c1+1
%p A096451   else c3:= c3+1
%p A096451   fi
%p A096451 od:
%p A096451 Res; # _Robert Israel_, Nov 07 2018
%Y A096451 Cf. A096447-A096455.
%Y A096451 Cf. A002144, A002145, A007350, A007351
%K A096451 nonn
%O A096451 1,1
%A A096451 _Yasutoshi Kohmoto_, Aug 12 2004
%E A096451 More terms from _Joshua Zucker_, May 03 2006