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 1-4 of 4 results.

A176684 Numbers k such that k^3 +-5 are primes.

Original entry on oeis.org

2, 12, 48, 66, 78, 126, 192, 324, 576, 738, 858, 1806, 2466, 2496, 2688, 3186, 3276, 3978, 4092, 4248, 4404, 4884, 5034, 5274, 5352, 5898, 6018, 6198, 6396, 6408, 6516, 6708, 6852, 7368, 7914, 8304, 8628, 8658, 8904, 9048, 9168, 9528, 10812, 10932
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Apr 23 2010

Keywords

Examples

			12 is in the sequence, because 12^3 - 5 = 1723 and 12^3 + 5 = 1733 are primes.

Links

Crossrefs

Cf. A090121, A097698, A108701, A143904, A176681, A176682, A176683

Programs

  • Mathematica
    Select[Range[8! ],PrimeQ[ #^3-5]&&PrimeQ[ #^3+5]&]

A176685 Numbers k such that k^3 +-7 are primes.

Original entry on oeis.org

36, 114, 174, 264, 426, 444, 810, 894, 900, 2724, 3876, 4140, 4386, 4446, 4686, 4884, 5910, 5940, 6240, 6294, 6534, 6624, 7044, 7206, 7314, 7326, 7470, 8076, 8676, 9120, 9216, 9270, 9546, 9900, 10926, 11040, 11934, 12114, 12510, 14004, 14034, 14100
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Apr 23 2010

Keywords

Examples

			36 is in the sequence, because 36^3 - 7 = 46649 and 36^3 + 7 = 46663 are primes.

Links

Crossrefs

Cf. A090121, A097698, A108701, A143904, A176681, A176682, A176683, A176684

Programs

  • Mathematica
    Select[Range[8! ],PrimeQ[ #^3-7]&&PrimeQ[ #^3+7]&]
Select[Range[15000],AllTrue[#^3+{7,-7},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 28 2020 *)

A248738 Least number m such that both m^2 -/+ prime(n) are (positive) primes.

Original entry on oeis.org

3, 4, 6, 6, 90, 4, 6, 30, 6, 180, 6, 12, 30, 18, 12, 48, 60, 90, 24, 30, 18, 120, 12, 510, 10, 60, 36, 12, 60, 12, 12, 30, 12, 12, 30, 120, 24, 48, 18, 48, 690, 1020, 30, 14, 18, 420, 180, 18, 36, 540, 42, 1230, 150, 870, 36, 18, 330, 870, 18, 30, 18, 18, 18, 150, 30, 18, 30, 30, 60, 180, 24, 30, 36
Offset: 1

Views

Author

Zak Seidov, Oct 13 2014

Keywords

Examples

			a(1)=3 because p=prime(1)=2 and both P=3^2-2=7 and Q=3^2+2=11 are prime;
a(3)=6 because p=5 and both P=31 and Q=41 are prime;
a(10000)=510 because p=104729 and both P=155371 and Q=364829 are prime.

Links

Crossrefs

Cf. A108701, A153975, A176681, A176682, A176683, A177833.

Programs

  • Mathematica
    lnm[n_]:=Module[{m=2,pr=Prime[n]},If[m^2-pr<0,m=Ceiling[Sqrt[pr]]];While[ !AllTrue[m^2+{pr,-pr},PrimeQ],m++];m]; Array[lnm,80] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Nov 22 2014 *)
  • PARI
    a(n) = { p = prime(n); m = sqrtint(p); until( isprime(m^2-p) && isprime(m^2+p), m++); m} \\ Michel Marcus, Oct 13 2014

A248790 Numbers n with the property that p = n^2 - 11 and q = n^2 + 11 are consecutive primes.

Original entry on oeis.org

510, 720, 1200, 2190, 4350, 4980, 5040, 5250, 5670, 6810, 8280, 8490, 9150, 10140, 10650, 11430, 12510, 13800, 13980, 14160, 14640, 14700, 14820, 15000, 15750, 16890, 17220, 18180, 18270, 18750, 19110, 20940, 21270, 22050, 24000, 24570, 24720, 24990, 25620, 25920, 26520
Offset: 1

Views

Author

Zak Seidov, Oct 14 2014

Keywords

Comments

All terms are == 0 (mod 30).

Examples

			n=510, p=260089=prime(22845), q=260111=prime(22846).

Links

Crossrefs

Subsequence of A176683 and of A075190. E.g., a(1)=510=A075190(62)=A176683(6).
Cf. A248785.

Programs

  • Mathematica
    Select[Range[30000],With[{c=#^2-11},PrimeQ[c]&&NextPrime[c]==c+22&]] (* Harvey P. Dale, Apr 03 2025 *)
  • PARI
    isok(n) = isprime(p=n^2-11) && isprime(q=n^2+11) && (q==nextprime(p+1)); \\ Michel Marcus, Oct 14 2014
Showing 1-4 of 4 results.

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