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.

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;

A336738 Primes abs(A335592(k))/2 for k in A335593.

Original entry on oeis.org

1399, 17939, 32869, 149759, 282349, 458929, 388099, 615389, 634169, 585619, 926179, 1053449, 1876339, 1336529, 2056829, 2156369, 2695249, 2653699, 2819779, 2501449, 1461709, 2176679, 3457969, 2549479, 3433819, 5299219, 4845499, 4774619, 7874749, 8796049, 9139469, 9029399, 7075759, 5156299
Offset: 1

Views

Author

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

Keywords

Comments

All terms end in 9 (or 1, if there are any with A335592(k) < 0).

Examples

			A335593(3) = 27, A335592(27) = det(631, 563; 577, 619) = 65738 = 2*32869
so a(3) = 32869.

Links

Crossrefs

Cf. A335592, A335593.

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, abs(v)/2; fi
od:
R;

Formula

a(n) = abs(A335592(A335593(n)))/2.

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.

Original entry on oeis.org

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

Views

Author

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

Keywords

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

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;
Showing 1-3 of 3 results.

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

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