A163431 -id:A163431 - cp's OEIS frontend

A163430 Primes of the form floor(p^3/8), where p is any prime number.

3, 857, 71473, 716917, 870983, 1706489, 6486889, 10007873, 33230963, 46461869, 50447927, 86058173, 177030983, 190605743, 200715401, 236602381, 263991523, 364759573, 388218197, 581137663, 742446841, 1081625359, 1129738223

Offset: 1

Vladimir Joseph Stephan Orlovsky, Jul 27 2009

nonn

			From p=3, 3^3/8=3.375 contributes a(1)=3. p=19, 19^3/8 = 857.275 contributes a(2) = 857.

J. Mulder, Table of n, a(n) for n = 1..10000

f[n_]:=IntegerPart[(p/2)^3]; lst={};Do[p=Prime[n];If[PrimeQ[f[p]],AppendTo[lst, f[p]]],{n,7!}];lst
Select[Floor[#^3/8]&/@Prime[Range[500]],PrimeQ] (* Harvey P. Dale, Apr 11 2012 *)

a(n) = floor( A163431(n)^3/8).

Mathematica-specific notation removed, comments moved to examples - R. J. Mathar, Sep 17 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

A163430 Primes of the form floor(p^3/8), where p is any prime number.

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

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

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