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.

A176582 n^2+Largest cube, (Largest cube <= n^2).

Original entry on oeis.org

0, 2, 5, 17, 24, 33, 63, 76, 128, 145, 164, 185, 269, 294, 321, 441, 472, 505, 540, 704, 743, 784, 827, 1041, 1088, 1137, 1188, 1458, 1513, 1570, 1629, 1690, 2024, 2089, 2156, 2225, 2296, 2700, 2775, 2852, 2931, 3012, 3492, 3577, 3664, 3753, 3844, 4406
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Apr 21 2010

Keywords

Comments

9+8=17, 16+8=24, 25+8=33, 36+27=63,..

Crossrefs

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

Programs

  • Mathematica
    r[n_]:=n^2;f[n_]:=r[n]+Floor[r[n]^(1/3)]^3;Table[f[n],{n,0,5!}]

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

Original entry on oeis.org

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

Views

Author

Vladimir Joseph Stephan Orlovsky, Apr 21 2010

Keywords

Comments

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

Crossrefs

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

Programs

  • Mathematica
    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

Views

Author

Vladimir Joseph Stephan Orlovsky, Apr 21 2010

Keywords

Comments

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

Links

Crossrefs

Primes in A176580.
Cf. A065733, A075847, A077116, A176581, A176582, A176583.

Programs

  • Maple
    g:= n -> n + floor(sqrt(n))^2:
select(isprime,map(g,[seq(i^3,i=1..1000)])); # Robert Israel, Jan 10 2024
  • Mathematica
    r[n_]:=n^3;f[n_]:=r[n]+Floor[Sqrt[r[n]]]^2;Select[Table[f[n],{n,0,6!}],PrimeQ[ # ]&]
  • PARI
    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

Views

Author

Vladimir Joseph Stephan Orlovsky, Apr 21 2010

Keywords

Comments

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

Crossrefs

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

Programs

  • Mathematica
    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

Views

Author

Vladimir Joseph Stephan Orlovsky, Apr 21 2010

Keywords

Links

Crossrefs

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

Programs

  • Mathematica
    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 *)
  • PARI
    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
Showing 1-5 of 5 results.

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