A337145 - OEIS

%I #21 Jun 03 2024 18:36:26

%S 104,800,1712,2592,3760,4840,5728,12848,15664,18424,20888,23520,28232,

%T 28560,25320,30280,37248,50520,43680,33664,61560,73920,70544,57696,

%U 38696,27408,79280,63392,107328,109536,162608,172296,187352,197040,248064,228320,215912,229152,255480,231304,286408,256320

%N a(n) is the determinant of the 2 X 2 matrix whose entries (when read by rows) are the n-th primes congruent to 1, 3, 5, 7 mod 8 respectively.

%C The first negative term is a(20750) = -58207896.

%C All terms are divisible by 8.

%H Robert Israel, <a href="/A337145/b337145.txt">Table of n, a(n) for n = 1..30000</a>

%e The first primes == 1, 3, 5, 7 (mod 8) are 17, 3, 5, 7 respectively, so a(1) = 17*7 - 3*5 = 104.

%e The second primes == 1, 3, 5, 7 (mod 8) are 41, 11, 13, 23 respectively, so a(2) = 41*23 - 11*13 = 800.

%e The third primes == 1, 3, 5, 7 (mod 8) are 73, 19, 29, 31 respectively, so a(3) = 73*31 - 19*29 = 1712.

%p R:= NULL:

%p L:= [-7, -5, -3, -1]:

%p found:= false:

%p for k from 1 to 100 do

%p   for i from 1 to 4 do

%p    for x from L[i]+8 by 8 do until isprime(x);

%p    L[i]:= x;

%p   od;

%p   v:= L[1]*L[4]-L[2]*L[3];

%p   R:= R,v;

%p od:

%p R;

%Y Cf. A335581, A335592, A337146, A337147.

%Y Cf. A007519, A007520, A007521, A007522.

%K sign,look

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Jan 27 2021