A163427 -id:A163427 - cp's OEIS frontend

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

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

Vladimir Joseph Stephan Orlovsky, Jul 27 2009

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

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

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

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

lista(nn) = forprime(p=3, nn, if (isprime(q=((p+1)/2)^3 + ((p-1)/2)^2), print1(q, ", "))); \\ Michel Marcus, Oct 11 2016

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

Vladimir Joseph Stephan Orlovsky, Jul 27 2009

nonn

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

G. C. Greubel, Table of n, a(n) for n = 1..1000

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

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 *)

forprime(p=2,1e3,n=p^3\27;if(isprime(n),print1(n",")))

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

Vladimir Joseph Stephan Orlovsky, Jul 27 2009

nonn

			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.

G. C. Greubel, Table of n, a(n) for n = 1..1000

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

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

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

cp's OEIS Frontend

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

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

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Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

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

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Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Extensions