cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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.

Original entry on oeis.org

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

Views

Author

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

Keywords

Comments

All terms == 8 (mod 10).
Are there negative terms? The first 10^7 are positive.

Examples

			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.

Links

Crossrefs

Cf. A335581, A335593, A336738.

Programs

  • 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;

A335593 Numbers k such that abs(A335592(k))/2 is prime.

Original entry on oeis.org

4, 17, 27, 53, 74, 91, 97, 108, 111, 139, 152, 171, 207, 242, 245, 247, 275, 280, 286, 292, 310, 323, 352, 355, 385, 398, 424, 430, 471, 476, 484, 504, 525, 551, 555, 561, 586, 615, 626, 658, 659, 705, 709, 736, 744, 754, 772, 823, 837, 841, 849, 858, 866, 869, 870, 877, 882, 896, 937, 960, 995
Offset: 1

Views

Author

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

Keywords

Examples

			a(3) = 27 is a term because A335592(27) = det(631, 563; 577, 619) = 65738 = 2*32869 and 32869 is prime.

Links

Crossrefs

Cf. A335592, A336738.

Programs

  • Maple
    count:= 0: R:= NULL:
L:= [-9,-7,-3,-1]:
for k from 1 while count < 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;
  v:= L[1]*L[4]-L[2]*L[3];
  if isprime(abs(v)/2) then count:= count+1; R:= R, k; fi
od:
R;

A337147 Primes abs(A337145(k))/8 for k in A337146.

Original entry on oeis.org

13, 3529, 35801, 38447, 36299, 29399, 30757, 29389, 109211, 101141, 82037, 119737, 203227, 203381, 237143, 439753, 197677, 329533, 391337, 611449, 697757, 1082233, 840347, 1054213, 1154893, 1044343, 1249139, 962587, 990287, 1012861, 1051181, 1060051, 753847, 1182737, 889237, 605333, 769997
Offset: 1

Views

Author

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

Keywords

Examples

			A337146(3) = 41 with A337145(41) = det(1097, 883; 877, 967) = 286408 = 8*35801 so a(3) = 35801.

Links

Crossrefs

Cf. A336738, A337145, A337146.

Programs

  • Maple
    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, v; fi
od:
R;
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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