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.

A163427 Primes p such that (p+1)^3/8+(p-1)/2 is also prime.

Original entry on oeis.org

5, 7, 13, 19, 29, 31, 41, 53, 71, 101, 103, 109, 173, 191, 199, 223, 229, 233, 239, 257, 269, 277, 331, 383, 397, 431, 491, 569, 571, 599, 619, 631, 719, 733, 751, 757, 761, 823, 857, 859, 863, 887, 907, 937, 967, 971, 977, 1009, 1019, 1063, 1069, 1123, 1163
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jul 27 2009

Keywords

Comments

Primes A000040(k) such that (A006254(k-1))^3+ A005097(k-1) is also prime.

Examples

			For p=5, (5+1)^3/8+(5-1)/2=27+2=29, prime, which adds p=5 to the sequence.
For p=7, (7+1)^3/8+(7-1)/2=67, prime, which adds p=7 to the sequence.

Links

Crossrefs

Cf. A162652, A163418, A163419, A163420, A163421, A163422, A163424, A163425, A163426.

Programs

  • Magma
    [p: p in PrimesInInterval(3, 1200) | IsPrime((p+1)^3 div 8+(p-1) div 2)]; // Vincenzo Librandi, Apr 09 2013
  • Mathematica
    f[n_]:=((p+1)/2)^3+((p-1)/2); lst={};Do[p=Prime[n];If[PrimeQ[f[p]],AppendTo[lst, p]],{n,6!}];lst
Select[Prime[Range[100]], PrimeQ[(# + 1)^3 / 8 + (# - 1) / 2]&] (* Vincenzo Librandi, Apr 09 2013 *)

Formula

(a(n)+1)^3/8+(a(n)-1)/2 = A163426(n).

Extensions

Edited by R. J. Mathar, Aug 24 2009

A163428 Primes of the form ((p+1)/2)^3 + ((p-1)/2)^2 where p is prime.

Original entry on oeis.org

31, 73, 241, 379, 3571, 9661, 20359, 47881, 51949, 65521, 119953, 135151, 291721, 427351, 736921, 761671, 921889, 1202041, 1494313, 1533871, 1742161, 1785961, 2478331, 2533681, 3197839, 3820441, 3894229, 4044643, 4855033, 6573799
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jul 27 2009

Keywords

Comments

Primes of the form k^3 + k^2 - 2k + 1 where 2k-1 is prime.

Examples

			((5+1)/2)^3 + ((5-1)/2)^2 = 27 + 4 = 31, ((7+1)/2)^3 + ((7-1)/2)^2 = 64 + 9 = 73

Links

Crossrefs

Cf. A162652, A163418, A163419, A163420, A163421, A163422, A163424, A163425, A163426, A163427

Programs

  • Maple
    res:= NULL:
count:= 0:
p:= 2
while count < 100 do
  p:= nextprime(p);
  r:=  ((p+1)/2)^3 + ((p-1)/2)^2;
  if isprime(r) then
     res:= res, r;
     count:= count+1;
  fi
od:
res; # Robert Israel, Oct 10 2016
  • Mathematica
    f[n_]:=((p+1)/2)^3+((p-1)/2)^2; lst={}; Do[p=Prime[n]; If[PrimeQ[f[p]],AppendTo[lst,f[p]]],{n,6!}]; lst
  • PARI
    lista(nn) = forprime(p=3, nn, if (isprime(q=((p+1)/2)^3 + ((p-1)/2)^2), print1(q, ", "))); \\ Michel Marcus, Oct 11 2016

Extensions

Description and edits by Charles R Greathouse IV, Oct 05 2009

A163442 Primes of the form floor((p/3)^3), where p is prime.

Original entry on oeis.org

181, 1103, 40471, 143329, 212419, 266261, 468493, 14586401, 20948491, 48894061, 53298877, 86546399, 136061111, 150851969, 189448891, 227353303, 249650309, 256855171, 328033129, 361451309, 507533053, 710528249, 815653171, 1172016731
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jul 27 2009

Keywords

Examples

			(17/3)^3=181.963 -> 181, (31/3)^3=1103.37 -> 1103, (103/3)^3=40471.4 -> 40471

Links

Crossrefs

Cf. A162652, A163418, A163419, A163420, A163421, A163422, A163424, A163425, A163426, A163427, A163428, A163429, A163430, A163431.

Programs

  • Mathematica
    f[n_]:=IntegerPart[(p/3)^3]; lst={};Do[p=Prime[n];If[PrimeQ[f[p]],AppendTo[lst,f[p]]],{n,7!}];lst
Select[Table[Floor[(p/3)^3],{p,Prime[Range[800]]}],PrimeQ] (* Harvey P. Dale, Dec 16 2017 *)
  • PARI
    forprime(p=2,1e3,n=p^3\27;if(isprime(n),print1(n",")))

Extensions

Program and editing by Charles R Greathouse IV, Nov 09 2009

A163443 Primes p such that floor(p^3/27) is prime.

Original entry on oeis.org

17, 31, 103, 157, 179, 193, 233, 733, 827, 1097, 1129, 1327, 1543, 1597, 1723, 1831, 1889, 1907, 2069, 2137, 2393, 2677, 2803, 3163, 3257, 3433, 3617, 3797, 4261, 4999, 5233, 5237, 5309, 5449, 5701, 5939, 6079, 6173, 6637, 6781, 6961, 7069, 7321, 7879
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Jul 27 2009

Keywords

Examples

			p=17 is in the sequence because [(17/3)^3] = [181.963] = 181 is prime.
p=31 is in the sequence because [(31/3)^3] = [1103.37] = 1103 is prime.

Links

Crossrefs

Cf. A162652, A163418, A163419, A163420, A163421, A163422, A163424, A163425, A163426, A163427, A163428, A163429, A163430, A163431, A163442

Programs

  • Mathematica
    f[n_]:=IntegerPart[(p/3)^3]; lst={};Do[p=Prime[n];If[PrimeQ[f[p]],AppendTo[lst, p]],{n,7!}];lst

Extensions

Introduced standard terminology in the definition - R. J. Mathar, Aug 02 2009

A165945 Primes of the form p+(p+1)^3, where p is also prime.

Original entry on oeis.org

29, 67, 5849, 3375149, 7078079, 7762589, 11852579, 17173769, 42144539, 46656359, 80621999, 87528827, 91125449, 102503699, 132651509, 142237169, 173741669, 264609929, 287496659, 320014187, 567664379, 686129849, 700227959, 851972339
Offset: 1

Views

Author

Claudio Meller, Oct 01 2009

Keywords

Comments

Generated by p=2, 3, 17, 149, 191, 197, 227, 257 etc.

Links

Crossrefs

Cf. A163426. - R. J. Mathar, Oct 28 2009

Programs

  • Magma
    [a: p in PrimesInInterval(1, 1000) | IsPrime(a) where a is p + (p + 1)^3]; // Vincenzo Librandi, Oct 12 2012
  • Mathematica
    Select[Table[p + (p + 1)^3, {p, Prime[Range[300]]}], PrimeQ] (* Vincenzo Librandi, Oct 12 2012 *)

Extensions

Definition shortened by R. J. Mathar, Oct 28 2009
Showing 1-5 of 5 results.

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