A337147 -id:A337147 - cp's OEIS frontend

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

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

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

All terms are divisible by 8.

			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.

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

Cf. A335581, A335592, A337146, A337147.

Cf. A007519, A007520, A007521, A007522.

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;

A337146 Numbers k such that abs(A337145(k))/8 is prime.

Original entry on oeis.org

1, 13, 41, 50, 53, 62, 67, 76, 89, 98, 108, 113, 137, 180, 211, 225, 236, 240, 250, 281, 293, 300, 303, 308, 355, 362, 384, 392, 393, 400, 414, 425, 434, 458, 468, 477, 489, 525, 588, 589, 593, 625, 653, 662, 664, 671, 673, 674, 696, 698, 732, 758, 765, 795, 800, 819, 831, 851, 880, 916, 933, 938

Offset: 1

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

nonn

			a(3) = 41 is a term because A337145(41) = det(1097, 883; 877, 967) = 286408 = 8*35801 and 35801 is prime.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A335593, A337145, A337147.

R:= NULL:
count:= 0:
L:= [-7, -5, -3, -1]:
for k from 1 while count < 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:= abs(L[1]*L[4]-L[2]*L[3])/8;
  if isprime(v) then count:= count+1; R:= R, k; fi
od:
R;

cp's OEIS Frontend

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.

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