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.

Previous Showing 11-15 of 15 results.

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

A268475 Numbers n such that n^3 +/- 2 and 3*n +/- 2 are all prime.

Original entry on oeis.org

435, 555, 2415, 31635, 38025, 44835, 80625, 88335, 97455, 98505, 99435, 124335, 142065, 145095, 165375, 176055, 204765, 246435, 279225, 293475, 310095, 315555, 332085, 344745, 348735, 376935, 392415, 443595, 462105, 467385, 482355, 581415, 609555, 626775, 636015
Offset: 1

Views

Author

K. D. Bajpai, Feb 05 2016

Keywords

Comments

All the terms in this sequence are congruent to 0 (mod 5).
Each term in this sequence yields two sets of cousin prime pairs i.e., for n = 435 -> {82312877, 82312873} and {1307, 1303}.
All terms are congruent to 15 mod 30. - Robert Israel, Feb 05 2016

Examples

			435 is in the sequence because 435^3 + - 2 =  82312877, 82312873; 3*435 + - 2 = 1307, 1303 are all prime.
555 is in the sequence because 555^3 + - 2 =  170953877, 170953873; 3*555 + - 2 = 1667, 1663 are all prime.

Links

Crossrefs

Cf. A024893, A090121, A108701, A153183, A157834.

Programs

  • Magma
    [n : n in [1..1e5] | IsPrime(n^3 + 2) and IsPrime(n^3 - 2) and IsPrime(3*n + 2) and IsPrime(3*n - 2)];
  • Maple
    select(n -> andmap(isprime, [n^3 + 2, n^3 - 2, 3*n + 2, 3*n - 2]), [seq(p, p=1.. 10^6)]);
  • Mathematica
    Select[Range[1000000], PrimeQ[#^3 + 2] && PrimeQ[#^3 - 2] && PrimeQ[3 # + 2] && PrimeQ[3 # - 2] &]
  • PARI
    for(n = 1,1e5, if( isprime(n^3 + 2) && isprime(n^3 - 2) && isprime(3*n + 2) && isprime(3*n - 2), print1(n ", ")))

A330438 Numbers k such that k^2-2 and k^3-2 are prime.

Original entry on oeis.org

9, 15, 19, 27, 37, 121, 135, 145, 211, 217, 259, 265, 267, 279, 355, 357, 387, 391, 435, 489, 525, 561, 615, 621, 727, 951, 987, 1029, 1119, 1141, 1177, 1251, 1287, 1357, 1435, 1491, 1561, 1617, 1717, 1785, 1819, 1839, 1875, 1909, 1989, 2001, 2077, 2107, 2211
Offset: 1

Views

Author

K. D. Bajpai, Dec 14 2019

Keywords

Comments

Intersection of A028870 and A038599.

Examples

			a(1) = 9: 9^2 - 2 = 79; 9^3 - 2 = 727; both results are prime.
a(2) = 15: 15^2 - 2 = 223; 15^3 - 2 = 3373; both results are prime.

Links

Crossrefs

Cf. A028870, A028873, A038599, A038600, A108701.

Programs

  • Magma
    [n : n in [1 .. 100] | IsPrime (n^2 - 2) and IsPrime (n^3 - 2)];
  • Maple
    filter:= k -> isprime(k^2-2) and isprime(k^3-2):
select(filter, [$2..10000]); # Robert Israel, Dec 24 2019
  • Mathematica
    Select[Range[10000], PrimeQ[#^3 - 2] && PrimeQ[#^2 - 2] &]

A155023 Values of n such that n^a-+a are primes, a=11.

Original entry on oeis.org

0, 1770, 10182, 11700, 12090, 16548, 24192, 27570, 29142, 29148, 60648, 62790, 63120, 97110, 104502, 115140, 116718, 119682, 122130, 127728, 147210, 151848, 170292, 189318, 190452, 192738
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jan 19 2009

Keywords

Crossrefs

Cf. A108701, A143904, A155021, A155022

Programs

  • Mathematica
    a={};Do[m=n^11;If[PrimeQ[m-11]&&PrimeQ[m+11],AppendTo[a,n]],{n,0,9!}];a
Select[Range[0,200000],And@@PrimeQ[#^11+{11,-11}]&] (* Harvey P. Dale, Jun 20 2013 *)
Previous Showing 11-15 of 15 results.

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