%I #32 May 31 2024 03:53:07
%S 5,11,17,23,31,41,47,59,67,103,127,419,431,439,461,467,1259,1279,1303,
%T 26833,26849,26881,26893,26921,26947,615883,616769,616787,616793,
%U 616829,617051,617059,617087,617257,617473,617509,617647,617681,617731,617819,617879
%N Primes p such that the number of primes less than p equal to 1 mod 4 is one less than the number of primes less than p equal to 3 mod 4.
%H Michel Marcus, <a href="/A096448/b096448.txt">Table of n, a(n) for n = 1..751</a>
%e First term prime(2) = 3 is placed on 0th row.
%e If prime(n-1) = +1 mod 4 is on k-th row then we put prime(n) on (k-1)-st row.
%e If prime(n-1) = -1 mod 4 is on k-th row then we put prime(n) on (k+1)-st row.
%e This process makes an array of prime numbers:
%e 0th row: 3, 7, 19, 43, ...
%e 1st row: 5, 11, 17, 23, 31, 41, 47, 59, 67, 103, 127, ...
%e 2nd row: 13, 29, 37, 53, 61, 71, 79, 101, 107, 113 ...
%e 3rd row: 73, 83, 97, 109, ...
%e 4th row: 89, ...
%t Prime[#]&/@(Flatten[Position[Accumulate[If[Mod[#,4]==1,1,-1]&/@ Prime[ Range[ 2,51000]]],-1]]+2) (* _Harvey P. Dale_, Mar 08 2015 *)
%o (PARI) lista(nn) = my(vp=primes(nn), nb1=0, nb3=0); for (i=2, #vp, my(p = vp[i]); if (nb1 == nb3-1, print1(p, ", ")); if ((p % 4) == 1, nb1++, nb3++);); \\ _Michel Marcus_, May 30 2024
%Y Cf. A096447, A096449, A096450, A096451, A096452, A096453, A096454, A096455.
%K nonn
%O 1,1
%A _Yasutoshi Kohmoto_, Aug 12 2004
%E More terms from _Joshua Zucker_, May 03 2006