A335592 a(n) is the determinant of the 2 X 2 matrix whose entries (when read by rows) are the n-th primes ending in 1, 3, 7, 9 respectively.

188, 678, 1568, 2798, 2768, 3928, 9328, 9418, 16918, 12418, 19428, 19578, 16898, 34698, 28028, 30988, 35878, 58528, 53908, 52318, 54938, 37308, 53098, 49888, 49758, 68688, 65738, 74328, 96558, 100098, 95548, 121898, 119108, 117438, 104078, 140698, 156588, 143168, 222888, 226608, 196448, 160448

Offset

1,1

Comments

All terms == 8 (mod 10).

Are there negative terms? The first 10^7 are positive.

Links

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

Example

The first primes ending in 1,3,7,9 are 11,3,7,19, so a(1) = 11*19 - 3*7 = 188.
The second primes ending in 1,3,7,9 are 31,13,17,29, so a(2) = 31*29 - 13*17 = 678.
The third primes ending in 1,3,7,9 are 41,23,37,59, so a(3) = 41*59 - 23*37 = 1568.

Maple

R:= NULL:
L:= [-9, -7, -3, -1]:
for k from 1 to 100 do
  for i from 1 to 4 do
   for x from L[i]+10 by 10 do until isprime(x);
   L[i]:= x;
  od;
  R:= R, L[1]*L[4]-L[2]*L[3];
od:
R;

Crossrefs

Cf. A335581, A335593, A336738.

Sequence in context: A304279 A099945 A211814 * A233786 A233961 A073586

Adjacent sequences: A335589 A335590 A335591 * A335593 A335594 A335595

Keyword

nonn,base,look

Author

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

Status

approved