A096447 - OEIS

%I #38 Jun 02 2024 10:17:44

%S 3,7,19,43,463,26839,26861,26879,26891,26903,26927,616783,616799,

%T 616841,616849,616877,617039,617269,617369,617401,617429,617453,

%U 617471,617479,617521,617537,617587,617689,617717,617723,618439,618547,618619,618643

%N Odd primes p such that the number of primes less than p that are congruent to 1 (mod 4) is equal to the number of primes less than p that are congruent to 3 (mod 4).

%C Assign the odd prime numbers to the rows of an array as follows:

%C Assign the first odd prime, prime(2) = 3, to row 0 (the top row).

%C For m > 2, assign prime(m) to the row immediately above or below the row to which prime(m-1) was assigned: above if prime(m-1) == 1 (mod 4), below otherwise.

%C The following array results:

%C   row 0 (this sequence): 3, 7, 19, 43, 463, 26839, ...

%C   row 1 (A096448):       5, 11, 17, 23, 31, 41, 47, 59, 67, 103, 127, ...

%C   row 2 (A096451):       13, 29, 37, 53, 61, 71, 79, 101, 107, 113 ...

%C   row 3:                 73, 83, 97, 109, ...

%C   row 4:                 89, ...

%H Giovanni Resta, <a href="/A096447/b096447.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A151800(A007351(n)), the next prime after A007351(n). - _Joshua Zucker_, May 03 2006

%t lim = 10^5; k1 = 0; k3 = 0; p = 2; t = {}; Do[p = NextPrime[p]; If[k1 == k3, AppendTo[t, p]]; If[Mod[p, 4] == 1, k1++, k3++], {lim}]; t (* _T. D. Noe_, Sep 07 2011 *)

%Y Cf. A007351, A151800.

%Y Cf. A096448, A096449, A096450, A096451, A096452, A096453, A096454, A096455.

%K nonn,easy

%O 1,1

%A _Yasutoshi Kohmoto_, Aug 12 2004

%E More terms from _Joshua Zucker_, May 03 2006

%E "odd" added to definition by _N. J. A. Sloane_, Sep 09 2015