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 1-6 of 6 results.

A091968 Primes congruent to 3 (mod 16).

Original entry on oeis.org

3, 19, 67, 83, 131, 163, 179, 211, 227, 307, 419, 467, 499, 547, 563, 643, 659, 691, 739, 787, 883, 947, 1091, 1123, 1171, 1187, 1283, 1427, 1459, 1523, 1571, 1619, 1667, 1699, 1747, 1811, 1907, 1987, 2003, 2083, 2099, 2131, 2179, 2243, 2339, 2371, 2467
Offset: 1

Views

Author

Giovanni Teofilatto, Mar 14 2004

Keywords

Comments

For any n, the equations x^4 - y^4 = a(n)*z^2 and x^4 - a(n)^2*y^4 = z^2 are not solvable in natural numbers. - Arkadiusz Wesolowski, Aug 15 2013

References

  • L. J. Mordell, Diophantine Equations, Ac. Press, p. 23.
  • Trygve Nagell, Introduction to Number Theory, Chelsea Publishing Company, NY, 1964, p. 230.

Crossrefs

Programs

Extensions

More terms from Ray Chandler, Mar 15 2004

A093012 Numbers k such that prime(k) == 3 (mod 16).

Original entry on oeis.org

2, 8, 19, 23, 32, 38, 41, 47, 49, 63, 81, 91, 95, 101, 103, 117, 120, 125, 131, 138, 153, 161, 182, 188, 193, 195, 208, 225, 232, 241, 248, 256, 262, 266, 272, 280, 292, 300, 304, 314, 317, 321, 327, 334, 346, 351, 365, 370, 376, 385, 394, 409, 410, 414, 427
Offset: 1

Views

Author

Ray Chandler, Mar 15 2004, revised Nov 06 2006

Keywords

Comments

A091968 indexed by A000040.
The asymptotic density of this sequence is 1/8 (by Dirichlet's theorem). - Amiram Eldar, Mar 01 2021

Crossrefs

Programs

  • Magma
    [n: n in [1..450]|(NthPrime(n) mod 16) eq 3] // G. C. Greubel, Feb 05 2019
    
  • Mathematica
    Select[Range[430], Mod[Prime[ # ], 16] == 3 &] (* Ray Chandler, Nov 06 2006 *)
  • PARI
    {isok(n) = Mod(prime(n), 16)==3};
    for(n=1, 450, if(isok(n)==1, print1(n, ", "), 0)) \\ G. C. Greubel, Feb 05 2019

Formula

A000040(a(n)) = A091968(n).
a(n) = A000720(A091968(n)).

A123990 Numbers k for which 16*k+1, 16*k+3, 16*k+7, 16*k+13 and 16*k+15 are primes.

Original entry on oeis.org

1, 7771, 18166, 21691, 26146, 26356, 46801, 69046, 75916, 91516, 111406, 122716, 156196, 171436, 175726, 177316, 201571, 219316, 222706, 259951, 282826, 355531, 426796, 433621, 435301, 438976, 440056, 524371, 560461, 585166, 605506, 608026
Offset: 1

Views

Author

Artur Jasinski, Oct 30 2006

Keywords

Crossrefs

Cf. A092022.

Programs

  • Mathematica
    Select[Range[10^6], And @@ PrimeQ /@ ({1, 3, 7, 13, 15} + 16#) &] (* Ray Chandler, Dec 06 2006 *)

A123992 Numbers k such that 16*k+1, 16*k+3 and 16*k+13 are primes.

Original entry on oeis.org

1, 40, 106, 133, 250, 265, 271, 280, 295, 313, 418, 580, 691, 736, 748, 826, 946, 1231, 1240, 1435, 1471, 1561, 1756, 2023, 2035, 2038, 2101, 2575, 2728, 2878, 2926, 3268, 3400, 3451, 3688, 3715, 3883, 4213, 4306, 4726, 4936, 5080, 5398, 5761, 5908, 6046
Offset: 1

Views

Author

Artur Jasinski, Oct 30 2006

Keywords

Crossrefs

Cf. A092022.

Programs

  • Maple
    a:=proc(n) if isprime(16*n+1)=true and isprime(16*n+3)=true and isprime(16*n+13)=true then n else fi end: seq(a(n),n=1..5000); # Emeric Deutsch, Nov 03 2006
  • Mathematica
    Select[Range[6100], And @@ PrimeQ /@ ({1, 3, 13} + 16#) &] (* Ray Chandler, Nov 05 2006 *)

Extensions

Extended by Ray Chandler, Nov 05 2006

A123997 Numbers k for which 16*k+1, 16*k+3 and 16*k+15 are primes.

Original entry on oeis.org

1, 133, 166, 208, 313, 418, 616, 691, 718, 1336, 1441, 1573, 1588, 1756, 2083, 2308, 2533, 2926, 2986, 3688, 3766, 3883, 4036, 4096, 4201, 4663, 5311, 5626, 5908, 6181, 7018, 7456, 7771, 7798, 8188, 8881, 9196, 9343, 9388, 9826, 10108, 10123, 10528
Offset: 1

Views

Author

Artur Jasinski, Oct 31 2006

Keywords

Crossrefs

Cf. A092022.

Programs

  • Mathematica
    Select[Range[11000], And @@ PrimeQ /@ ({1, 3, 15} + 16#) &] (* Ray Chandler, Nov 05 2006 *)

Extensions

Extended by Ray Chandler, Nov 05 2006

A153348 Numbers n such that 16*n+3 is not prime.

Original entry on oeis.org

2, 3, 6, 7, 9, 12, 15, 16, 17, 18, 20, 21, 22, 23, 24, 25, 27, 28, 30, 32, 33, 36, 37, 38, 39, 42, 44, 45, 47, 48, 50, 51, 52, 53, 54, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 67, 69, 71, 72, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 90, 92, 93, 94
Offset: 1

Views

Author

Vincenzo Librandi, Dec 24 2008

Keywords

Examples

			Triangle begins:
*;
*,*;
*,2,*;
*,*,*,*;
*,*,*,6,*;
*,*.*,*,*,*;
*,*,*,*,*,12,*;
3,*,*,*,*,*,*,*;
*,*,*,*,*,*,*,20,*;
*,*,9,*,*,*,*,*,*,*;
*,7,*,*,*,*,*,*,*,30,*;
*,*,*,*,17,*,*,*,*,*,*,*;
where * marks the non-integer values of (2*h*k + k + h - 1)/8 with h >= k >= 1.
		

Crossrefs

Cf. A092022.

Programs

  • Magma
    [n: n in [0..150] | not IsPrime(16*n + 3)]; // Vincenzo Librandi, Jan 13 2013
  • Mathematica
    Select[Range[200], !PrimeQ[16*# + 3]&] (* Vincenzo Librandi, Jan 13 2013 *)
Showing 1-6 of 6 results.