A176582 -id:A176582 - cp's OEIS frontend

A176583 n^2+Smallest cube, (Smallest cube >= n^2).

0, 2, 12, 36, 43, 52, 100, 113, 128, 206, 225, 246, 360, 385, 412, 568, 599, 632, 667, 873, 912, 953, 996, 1258, 1305, 1354, 1405, 1458, 1784, 1841, 1900, 1961, 2355, 2420, 2487, 2556, 2627, 3097, 3172, 3249, 3328, 3409, 3961, 4046, 4133, 4222, 4313, 4953

Offset: 1

Vladimir Joseph Stephan Orlovsky, Apr 21 2010

nonn

4+8=12, 9+27=36, 16+27=43,..

Cf. A065733, A075847, A077116, A176580, A176581, A176582

r[n_]:=n^2;f[n_]:=r[n]+Ceiling[r[n]^(1/3)]^3;Table[f[n],{n,0,5!}]
Table[n^2+Ceiling[Surd[n^2,3]]^3,{n,0,50}] (* Harvey P. Dale, Jun 04 2016 *)

A176584 Primes of the form p = k^3 + (largest square <= k^3).

Original entry on oeis.org

2, 194057, 601067, 1607173, 3283993, 3630257, 3721363, 4918999, 5255713, 5848307, 6749569, 9999907, 17992913, 20432729, 23393483, 34746203, 44845993, 73843813, 84277273, 107165033, 109735649, 120469409, 125138873, 130898927

Offset: 1

Vladimir Joseph Stephan Orlovsky, Apr 21 2010

nonn

Consider k = 4 * x^2 + 1, where the largest square <= k^3 is (8 * x^3 + 3 * x)^2. Bunyakowsky's conjecture implies there are infinitely many primes of the form (4 * x^2 + 1)^3 + (8 * x^3 + 3 * x)^2, and so that the sequence is infinite. The first term of this form is 93389778901 = a(165), corresponding to x = 30. - Robert Israel, Jan 10 2024

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

Primes in A176580.

Cf. A065733, A075847, A077116, A176581, A176582, A176583.

g:= n -> n + floor(sqrt(n))^2:
select(isprime,map(g,[seq(i^3,i=1..1000)])); # Robert Israel, Jan 10 2024

r[n_]:=n^3;f[n_]:=r[n]+Floor[Sqrt[r[n]]]^2;Select[Table[f[n],{n,0,6!}],PrimeQ[ # ]&]

select(isprime, vector(1000, n, n^3+sqrtint(n^3)^2)) \\ Michel Marcus, Jan 10 2024

A176585 Primes of the form n^3+Smallest square, (Smallest square >= n^3).

Original entry on oeis.org

2, 17, 269, 281233, 1770217, 1826609, 2520841, 3907529, 7595017, 8665471, 9828089, 11280377, 12259063, 17235221, 27654961, 54008809, 70583033, 75196799, 85018949, 87240233, 106316057, 111499057, 168061561, 176255669, 201105409

Offset: 1

Vladimir Joseph Stephan Orlovsky, Apr 21 2010

nonn

8+9=17, 5^3+12^2=269,..

Cf. A065733, A075847, A077116, A176580, A176581, A176582, A176583, A176584

r[n_]:=n^3;f[n_]:=r[n]+Ceiling[Sqrt[r[n]]]^2;Select[Table[f[n],{n,0,6!}],PrimeQ[ # ]&]
ssn3[n_]:=n^3+(Ceiling[Sqrt[n^3]])^2; Select[Array[ssn3,500],PrimeQ] (* Harvey P. Dale, Jun 23 2017 *)

A176586 Primes of the form : n^3 + Largest square + Smallest square, (Largest square <= n^3, Smallest square >= n^3).

Original entry on oeis.org

3, 222601, 2824933, 3573761, 4215749, 5183821, 6001997, 6592613, 7886597, 8592401, 9725393, 10127813, 10531813, 12751093, 13720661, 15263009, 18087529, 30232597, 52730113, 68727469, 79395353, 109787269, 139967461, 162040453

Offset: 1

Vladimir Joseph Stephan Orlovsky, Apr 21 2010

nonn

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A065733, A075847, A077116, A176580, A176581, A176582, A176583, A176584, A176585.

r[n_]:=n^3;f[n_]:=r[n]+Floor[Sqrt[r[n]]]^2+Ceiling[Sqrt[r[n]]]^2;Select[Table[f[n],{n,0,7!}],PrimeQ[ # ]&]
lsss[n_]:=Module[{c=n^3},c+Floor[Sqrt[c]]^2+Ceiling[Sqrt[c]]^2]; Select[Array[ lsss,1000],PrimeQ] (* Harvey P. Dale, Feb 22 2023 *)

print1(3);for(n=2,1e3,t=sqrtint(n^3);if(isprime(t=n^3+t^2+ (t+1)^2) && !issquare(n),print1(", "t))) \\ Charles R Greathouse IV, Apr 15 2012

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A176583 n^2+Smallest cube, (Smallest cube >= n^2).

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A176584 Primes of the form p = k^3 + (largest square <= k^3).

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A176585 Primes of the form n^3+Smallest square, (Smallest square >= n^3).

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Author

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Mathematica

A176586 Primes of the form : n^3 + Largest square + Smallest square, (Largest square <= n^3, Smallest square >= n^3).

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PARI