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.

104, 800, 1712, 2592, 3760, 4840, 5728, 12848, 15664, 18424, 20888, 23520, 28232, 28560, 25320, 30280, 37248, 50520, 43680, 33664, 61560, 73920, 70544, 57696, 38696, 27408, 79280, 63392, 107328, 109536, 162608, 172296, 187352, 197040, 248064, 228320, 215912, 229152, 255480, 231304, 286408, 256320

Offset: 1

Author

J. M. Bergot and Robert Israel, Jan 27 2021

Keywords

• sign
• look

Comments

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

All terms are divisible by 8.

Examples

			The first primes == 1, 3, 5, 7 (mod 8) are 17, 3, 5, 7 respectively, so a(1) = 17*7 - 3*5 = 104.
The second primes == 1, 3, 5, 7 (mod 8) are 41, 11, 13, 23 respectively, so a(2) = 41*23 - 11*13 = 800.
The third primes == 1, 3, 5, 7 (mod 8) are 73, 19, 29, 31 respectively, so a(3) = 73*31 - 19*29 = 1712.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..30000

Crossrefs

Cf. A335581, A335592, A337146, A337147.

Cf. A007519, A007520, A007521, A007522.

Programs

Maple

R:= NULL:
L:= [-7, -5, -3, -1]:
found:= false:
for k from 1 to 100 do
  for i from 1 to 4 do
   for x from L[i]+8 by 8 do until isprime(x);
   L[i]:= x;
  od;
  v:= L[1]*L[4]-L[2]*L[3];
  R:= R,v;
od:
R;