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A337145 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.

%I A337145 #21 Jun 03 2024 18:36:26
%S A337145 104,800,1712,2592,3760,4840,5728,12848,15664,18424,20888,23520,28232,
%T A337145 28560,25320,30280,37248,50520,43680,33664,61560,73920,70544,57696,
%U A337145 38696,27408,79280,63392,107328,109536,162608,172296,187352,197040,248064,228320,215912,229152,255480,231304,286408,256320
%N A337145 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 A337145 The first negative term is a(20750) = -58207896.
%C A337145 All terms are divisible by 8.
%H A337145 Robert Israel, <a href="/A337145/b337145.txt">Table of n, a(n) for n = 1..30000</a>
%e A337145 The first primes == 1, 3, 5, 7 (mod 8) are 17, 3, 5, 7 respectively, so a(1) = 17*7 - 3*5 = 104.
%e A337145 The second primes == 1, 3, 5, 7 (mod 8) are 41, 11, 13, 23 respectively, so a(2) = 41*23 - 11*13 = 800.
%e A337145 The third primes == 1, 3, 5, 7 (mod 8) are 73, 19, 29, 31 respectively, so a(3) = 73*31 - 19*29 = 1712.
%p A337145 R:= NULL:
%p A337145 L:= [-7, -5, -3, -1]:
%p A337145 found:= false:
%p A337145 for k from 1 to 100 do
%p A337145   for i from 1 to 4 do
%p A337145    for x from L[i]+8 by 8 do until isprime(x);
%p A337145    L[i]:= x;
%p A337145   od;
%p A337145   v:= L[1]*L[4]-L[2]*L[3];
%p A337145   R:= R,v;
%p A337145 od:
%p A337145 R;
%Y A337145 Cf. A335581, A335592, A337146, A337147.
%Y A337145 Cf. A007519, A007520, A007521, A007522.
%K A337145 sign,look
%O A337145 1,1
%A A337145 _J. M. Bergot_ and _Robert Israel_, Jan 27 2021