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.

Previous Showing 11-15 of 15 results.

A168487 Primes of the form 100n^3 + 27.

Original entry on oeis.org

127, 827, 6427, 12527, 34327, 219727, 491327, 1562527, 2438927, 3276827, 8518427, 16637527, 22698127, 43897627, 45653327, 51200027, 77868827, 119101627, 129502927, 140492827, 156089627, 177156127, 190662427, 251545627, 257135327
Offset: 1

Views

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 27 2009

Keywords

Comments

(1) These primes all with the end digits 2 and 7 are concatenations of two CUBIC numbers: "n^3 3^3".
(2) It is conjectured that sequence is infinite.

References

  • Harold Davenport, Multiplicative Number Theory, Springer-Verlag New-York 1980
  • Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications 2005
  • Friedhelm Padberg, Elementare Zahlentheorie, Spektrum Akademischer Verlag, 2. Auflage 1991

Crossrefs

A167535 Concatenation of two square numbers which give a prime
A168147 Primes of the form p = 1 + 10*n^3 for a natural number n
A168327 Primes of concatenated form p = "1 n^3"

Programs

  • Mathematica
    Select[100Range[140]^3+27,PrimeQ] (* Harvey P. Dale, Aug 22 2011 *)

Extensions

Edited by Charles R Greathouse IV, Apr 24 2010

A168540 Natural numbers n for which 100n^3 + 27 is prime.

Original entry on oeis.org

1, 2, 4, 5, 7, 13, 17, 25, 29, 32, 44, 55, 61, 76, 77, 80, 92, 106, 109, 112, 116, 121, 124, 136, 137, 142, 143, 149, 152, 154, 158, 161, 169, 170, 178, 190, 191, 196, 200, 208, 221, 223, 224, 227, 230, 245, 254, 259, 260, 262
Offset: 1

Views

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 29 2009

Keywords

Comments

It is conjectured that sequence is infinite.

Examples

			(1) 3^3+10^2*1^3=127=prime(31) gives a(1)=1
(2) 3^3+10^2*2^3=827=prime(144) gives a(2)=2
(3) 3^3+10^2*13^3=219727=prime(19588) gives a(6)=13

References

  • Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications 2005
  • Friedhelm Padberg, Elementare Zahlentheorie, Spektrum Akademischer Verlag, 2. Auflage 1991

Crossrefs

Cf. A168147 Primes of the form p = 1 + 10*n^3 for a natural number n
Cf. A168327 Primes of concatenated form p= "1 n^3"
Cf. A168375 Natural numbers n for which the concatenation p= "1 n^3"is prime

Programs

  • Mathematica
    Select[Range[300],PrimeQ[100#^3+27]&] (* Harvey P. Dale, May 10 2013 *)

Extensions

Edited by Charles R Greathouse IV, Apr 28 2010

A174229 Natural numbers n such that the concatenation n^3//1331, i.e., a cube and 11^3, is a prime number.

Original entry on oeis.org

2, 6, 8, 14, 21, 38, 39, 51, 54, 65, 68, 78, 80, 93, 104, 107, 114, 117, 119, 125, 135, 137, 146, 147, 152, 153, 158, 159, 167, 186, 206, 225, 243, 246, 248, 257, 258, 269, 270, 272, 278, 284, 290, 291, 306, 311, 317, 321, 323, 324, 369, 372, 387, 390, 399, 404, 410, 414, 425
Offset: 1

Views

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Mar 13 2010

Keywords

Comments

See comments and references for A174213.

Examples

			2^3 = 8, 81331 = prime(7958) => a(1) = 2;
6^3 = 216, 2161331 = prime(160048) => a(2) = 6.

Crossrefs

Cf. A168327, A168417, A173836, A174213.

Programs

  • PARI
    isok(n) = isprime(eval(concat(Str(n^3), Str(1331)))); \\ Michel Marcus, Jul 20 2017

Extensions

More terms from Michel Marcus, Jul 20 2017

A174409 Prime numbers p such that the concatenation p^3//1331 is a prime number.

Original entry on oeis.org

2, 107, 137, 167, 257, 269, 311, 317, 557, 593, 761, 773, 809, 911, 1103, 1151, 1283, 1289, 1481, 1487, 1559, 1709, 1787, 1931, 2111, 2141, 2243, 2339, 2357, 2657, 2687, 2777, 2909, 3137, 3209, 3251, 3359, 3371, 3389, 3449
Offset: 1

Views

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Mar 19 2010

Keywords

Comments

See comments at A174213.
p^3//1331 is the concatenation of the cubes of two primes.
With the exception of a(1)=2, each term is necessarily of the form 6*k-1.

Examples

			The first prime is 2; 2^3 = 8, and 81331 = prime(7958), so a(1)=2.
The smallest prime p > 2 such that p^3//1331 yields a prime is p=107: 107^3 = 1225043, and 12250431331 = prime(552342812), so a(2)=107.

Links

Crossrefs

Cf. A168327, A168417, A173836, A174213, A174260, A174229, A174355.

Programs

  • Magma
    [p: p in PrimesUpTo(5000) | IsPrime(Seqint(Intseq(1331) cat Intseq(p^3)))]; // Vincenzo Librandi, Mar 05 2018
  • Mathematica
    Select[Prime[Range[500]],PrimeQ[10000#^3+1331]&] (* Harvey P. Dale, May 30 2017 *)

A169586 Primes p in A168540 for which q = 3^3 + 10^2*p^3 (A168487) is prime.

Original entry on oeis.org

2, 5, 7, 13, 17, 29, 61, 109, 137, 149, 191, 223, 227, 269, 311, 331, 337, 359, 389, 397, 409, 433, 457, 467, 491, 587, 619, 653, 661, 709, 727
Offset: 1

Views

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Dec 02 2009

Keywords

Comments

It is conjectured that sequence is infinite

Examples

			(1) 3^3+10^2*2^3=827=prime(144) gives a(1)=2=prime(1)
(2) 3^3+10^2*5^3=12527=prime(1496) gives a(2)=5=prime(3)
(3) 3^3+10^2*13^3=219727=prime(19588) gives a(4)=13=prime(6)

References

  • Leonard E. Dickson: History of the Theory of numbers, vol. I, Dover Publications 2005
  • Theo Kempermann, Zahlentheoretische Kostproben, Harri Deutsch, 2. aktualisierte Auflage 2005
  • Arnold Scholz, Bruno Schoeneberg: Einführung in die Zahlentheorie, Walter de Gruyter, 5. Auflage 1973

Crossrefs

A000040 The prime numbers
A167535 Concatenation of two square numbers which give a prime
A168147 Primes of the form p = 1 + 10*n^3 for a natural number n
A168327 Primes of concatenated form p= "1 n^3"
A168375 Naturals n for which the concatenation p= "1 n^3"is prime
A168487 Primes of form p = 3^3 + 10^2*n^3 with a natural number n
A168540 Naturals n for which the concatenation p = 3^3 + 10^2*n^3 is prime
Previous Showing 11-15 of 15 results.

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