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 1-5 of 5 results.

A248019 Values of x in equation A142508(n)=x^2+13y^2.

Original entry on oeis.org

1, 12, 14, 14, 25, 27, 25, 14, 1, 40, 1, 27, 38, 40, 12, 14, 1, 53, 14, 1, 51, 40, 27, 64, 64, 14, 66, 64, 77, 77, 79, 66, 79, 77, 25, 38, 77, 40, 1, 79, 64, 53, 12, 92, 90, 51, 66, 77, 25, 64, 92, 77, 1, 79, 64, 53, 1, 103, 38, 12, 14, 53, 1, 77, 116, 79, 116, 92, 118, 118, 77, 103, 66, 118, 38
Offset: 1

Views

Author

Zak Seidov, Oct 06 2014

Keywords

Examples

			a(1)=1 because A142508(1)=53=1^2+13*2^2 (x=1,y=2);
a(2)=12 because A142508(2)=157=12^2+13*1^2 (x=12, y=1).

Crossrefs

Cf. A033210, A142508, A248221, A248019(values of y).

Programs

  • Mathematica
    f[n_] := FindInstance[n == x^2 + 13 y^2 && x > 0 && y > 0, {x, y}, Integers][[1, 1, 2]]; f@# & /@ Select[ Prime@ Range@ 1840, Mod[#, 52] == 1 &] (* Robert G. Wilson v, Oct 06 2014 *)

A248368 Primes p such that 52*p + 1 is prime.

Original entry on oeis.org

3, 13, 31, 43, 73, 109, 139, 151, 181, 193, 211, 223, 229, 283, 349, 379, 409, 421, 463, 523, 601, 619, 691, 769, 823, 853, 1021, 1033, 1069, 1153, 1231, 1279, 1303, 1453, 1459, 1471, 1531, 1663, 1693, 1723, 1741, 1783, 1831, 1873, 1933, 2029, 2131, 2251, 2269, 2293, 2593, 2671, 2749, 2791
Offset: 1

Views

Author

Zak Seidov, Oct 05 2014

Keywords

Comments

Or, primes in A248221. Subsequence of A248221. Note that a(1..6) coincide with A171517(1..6).

Links

Crossrefs

Cf. A033210, A142508, A171517, A248221.

Programs

  • Maple
    A248368:=n->`if`(isprime(52*n+1) and isprime(n), n, NULL): seq(A248368(n), n=1..4000); # Wesley Ivan Hurt, Oct 05 2014
  • Mathematica
    s = {}; Do[If[PrimeQ[1 + 52*(p = Prime[n])], AppendTo[s, p]], {n, 500}]; s
Select[Prime[Range[500]],PrimeQ[52#+1]&] (* Harvey P. Dale, Aug 15 2017 *)
  • PARI
    forprime(p=1,10^4,if(isprime(52*p+1),print1(p,", "))) \\ Derek Orr, Oct 05 2014

A248372 Numbers m such that both p = 52*m + 1 and q = 52*p + 1 are prime.

Original entry on oeis.org

36, 39, 60, 126, 171, 189, 195, 300, 315, 405, 420, 435, 504, 540, 570, 606, 720, 756, 816, 876, 960, 1089, 1221, 1224, 1260, 1329, 1365, 1371, 1389, 1404, 1530, 1554, 1674, 1740, 1785, 1791, 1914, 1959, 2085, 2244, 2304, 2334, 2376, 2451, 2454, 2520, 2631, 2646, 2715, 2799, 2976
Offset: 1

Views

Author

Zak Seidov, Oct 05 2014

Keywords

Comments

All terms are divisible by 3, because if m == 1 or 2 (mod 3), either q or p is divisible by 3.

Links

Crossrefs

Subsequence of A248221.
Cf. A033210, A142508, A171517, A248221, A248368.

Programs

  • Mathematica
    s={};Do[If[PrimeQ[p=52*n+1]&&PrimeQ[52*p+1],AppendTo[s,n]],{n,3000}];s
Select[Range[3000],AllTrue[{52#+1,53+2704#},PrimeQ]&] (* Harvey P. Dale, Mar 21 2025 *)
  • PARI
    for(n=1,10^4,p=52*n+1;if(isprime(p)&&isprime(52*p+1),print1(n,", "))) \\ Derek Orr, Oct 06 2014

A248409 Least prime of the form x^2+13*n^2.

Original entry on oeis.org

13, 53, 181, 233, 389, 757, 641, 857, 1069, 1301, 1609, 1873, 2213, 2549, 3121, 3329, 3761, 4261, 4729, 5209, 5737, 6301, 6977, 7489, 8161, 8837, 9733, 10193, 10937, 11701, 12497, 13313, 14173, 15053, 16069, 17137, 18121, 18773, 19777, 20809, 21997, 23053, 24137, 25169, 27109, 27509
Offset: 1

Views

Author

Zak Seidov, Oct 06 2014

Keywords

Comments

Subsequence of A033210 (Primes of the form x^2+13*y^2).

Examples

			a(1)=13 because the least prime of the form x^2+13*1^2 is 13 (at x=0).
a(100)=130121 because the least prime of the form x^2+13*100^2 is 130121 (at x=11).
a(200)=520361 because the least prime of the form x^2+13*200^2 is 520361 (at x=19).

Links

Crossrefs

Cf. A033210, A106856, A247881, A248221.

Programs

  • PARI
    a(n) = {x = 0; while (!isprime(p=x^2+13*n^2), x++); p;} \\ Michel Marcus, Oct 06 2014

A248408 Values of y in A142508(n) = x^2+13y^2.

Original entry on oeis.org

2, 1, 3, 5, 2, 4, 6, 9, 10, 1, 12, 10, 7, 7, 13, 13, 14, 2, 15, 16, 8, 13, 16, 5, 7, 19, 7, 11, 2, 6, 4, 13, 6, 8, 22, 21, 10, 21, 24, 10, 17, 20, 25, 3, 7, 22, 19, 16, 26, 21, 11, 18, 28, 18, 23, 26, 30, 10, 29, 31, 31, 28, 32, 24, 1, 24, 5, 21, 5, 7, 26, 18, 29, 11, 33, 20, 32, 35, 15, 28, 2, 22
Offset: 1

Views

Author

Zak Seidov, Oct 06 2014

Keywords

Examples

			a(1)=2 because A142508(1)=53=1^2+13*2^2 (x=1,y=2);
a(2)=1 because A142508(2)=157=12^2+13*1^2 (x=12, y=1).

Crossrefs

Cf. A033210, A142508, A248221, A248019(values of x).
Showing 1-5 of 5 results.

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