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.

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A139500 Primes of the form x^2 + 20x*y + y^2 for x and y nonnegative.

Original entry on oeis.org

97, 157, 229, 577, 661, 709, 829, 1453, 1549, 1609, 1621, 1873, 2017, 2137, 2473, 2677, 2689, 2797, 2953, 3001, 3037, 3217, 3301, 3433, 3457, 3613, 3733, 4093, 4261, 4273, 4357, 4513, 4621, 4657, 4801, 4933, 5113, 5281, 5437, 5641, 6229, 6301, 6337
Offset: 1

Views

Author

Artur Jasinski, Apr 24 2008

Keywords

Links

Crossrefs

Cf. A139489, A007645, A068228, A007519, A033212, A033212, A107152, A107008, A033215, A107145, A139490, A139491.

Programs

  • Mathematica
    a = {}; w = 20; k = 1; Do[Do[If[PrimeQ[n^2 + w*n*m + k*m^2], AppendTo[a, n^2 + w*n*m + k*m^2]], {n, m, 400}], {m, 1, 400}]; Union[a] (*Artur Jasinski*)
With[{nn=50},Take[Select[Union[Flatten[Table[x^2+20 x y +y^2,{x,0,2nn},{y,0,2nn}]]],PrimeQ],nn]] (* Harvey P. Dale, Nov 02 2022 *)

A139501 Primes of the form x^2 + 21x*y + y^2 for x and y nonnegative.

Original entry on oeis.org

23, 47, 73, 101, 131, 139, 163, 197, 233, 239, 271, 277, 311, 347, 349, 353, 397, 443, 461, 463, 491, 499, 541, 577, 587, 593, 647, 653, 691, 719, 739, 761, 809, 821, 823, 853, 859, 883, 929, 947, 967, 997, 1013, 1051, 1061, 1087, 1151, 1163, 1223, 1277
Offset: 1

Views

Author

Artur Jasinski, Apr 24 2008

Keywords

Links

Crossrefs

Cf. A139489, A007645, A068228, A007519, A033212, A033212, A107152, A107008, A033215, A107145, A139490, A139491.

Programs

  • Mathematica
    a = {}; w = 21; k = 1; Do[Do[If[PrimeQ[n^2 + w*n*m + k*m^2], AppendTo[a, n^2 + w*n*m + k*m^2]], {n, m, 400}], {m, 1, 400}]; Union[a] (*Artur Jasinski*)

A139503 Primes of the form x^2 + 23x*y + y^2 for x and y nonnegative.

Original entry on oeis.org

79, 109, 151, 211, 331, 379, 421, 499, 541, 571, 631, 709, 739, 751, 919, 991, 1009, 1051, 1129, 1171, 1201, 1381, 1429, 1471, 1549, 1579, 1621, 1759, 1789, 1801, 1831, 1999, 2011, 2179, 2221, 2251, 2269, 2311, 2389, 2521, 2671, 2689, 2731, 2851, 3019
Offset: 1

Views

Author

Artur Jasinski, Apr 24 2008

Keywords

Links

Crossrefs

Cf. A139489, A007645, A068228, A007519, A033212, A033212, A107152, A107008, A033215, A107145, A139490, A139491.

Programs

  • Mathematica
    a = {}; w = 23; k = 1; Do[Do[If[PrimeQ[n^2 + w*n*m + k*m^2], AppendTo[a, n^2 + w*n*m + k*m^2]], {n, m, 400}], {m, 1, 400}]; Union[a] (*Artur Jasinski*)

A139504 Primes of the form x^2 + 24x*y + y^2 for x and y nonnegative.

Original entry on oeis.org

53, 113, 157, 181, 257, 269, 313, 389, 433, 521, 641, 653, 757, 797, 829, 881, 1013, 1049, 1093, 1109, 1153, 1193, 1213, 1277, 1301, 1433, 1453, 1609, 1621, 1637, 1741, 1873, 1901, 1973, 2029, 2161, 2237, 2297, 2341, 2357, 2473, 2557, 2677, 2729, 2753
Offset: 1

Views

Author

Artur Jasinski, Apr 24 2008

Keywords

Links

Crossrefs

Cf. A139489, A007645, A068228, A007519, A033212, A033212, A107152, A107008, A033215, A107145, A139490, A139491.

Programs

  • Mathematica
    a = {}; w = 24; k = 1; Do[Do[If[PrimeQ[n^2 + w*n*m + k*m^2], AppendTo[a, n^2 + w*n*m + k*m^2]], {n, m, 400}], {m, 1, 400}]; Union[a] (*Artur Jasinski*)

A139507 Primes of the form x^2 + 27x*y + y^2 for x and y nonnegative.

Original entry on oeis.org

29, 59, 199, 239, 281, 349, 419, 431, 439, 521, 571, 631, 719, 811, 821, 919, 941, 1009, 1019, 1021, 1039, 1069, 1151, 1231, 1301, 1321, 1459, 1579, 1789, 1831, 1861, 1889, 1949, 1979, 2029, 2039, 2089, 2111, 2141, 2269, 2311, 2411, 2441, 2609, 2659, 2789
Offset: 1

Views

Author

Artur Jasinski, Apr 24 2008

Keywords

Links

Crossrefs

Cf. A139489, A007645, A068228, A007519, A033212, A033212, A107152, A107008, A033215, A107145, A139490, A139491.

Programs

  • Mathematica
    a = {}; w = 27; k = 1; Do[Do[If[PrimeQ[n^2 + w*n*m + k*m^2], AppendTo[a, n^2 + w*n*m + k*m^2]], {n, m, 400}], {m, 1, 400}]; Union[a] (*Artur Jasinski*)

A139508 Primes of the form x^2 + 28x*y + y^2 for x and y nonnegative.

Original entry on oeis.org

61, 181, 601, 829, 1069, 1249, 1381, 1429, 1609, 1621, 1741, 2029, 2089, 2161, 2341, 2389, 2521, 3121, 3169, 3181, 3301, 3709, 3769, 4021, 4261, 4549, 4729, 4801, 4861, 4969, 5209, 5281, 5521, 5581, 5641, 5749, 5821, 6301, 6361, 6421, 6529, 6709, 6829
Offset: 1

Views

Author

Artur Jasinski, Apr 24 2008

Keywords

Comments

In base 12, the sequence is 51, 131, 421, 591, 751, 881, 971, 9E1, E21, E31, 1011, 1211, 1261, 1301, 1431, 1471, 1561, 1981, 1X01, 1X11, 1XE1, 2191, 2221, 23E1, 2571, 2771, 28X1, 2941, 2991, 2X61, 3021, 3081, 3241, 3291, 3321, 33E1, 3451, 3791, 3821, 3871, 3941, 3X71, 3E51, where X is 10 and E is 11. Moreover, the discriminant is 550. - Walter Kehowski, Jun 01 2008

Links

Crossrefs

Cf. A139489, A007645, A068228, A007519, A033212, A033212, A107152, A107008, A033215, A107145, A139490, A139491.

Programs

  • Mathematica
    a = {}; w = 28; k = 1; Do[Do[If[PrimeQ[n^2 + w*n*m + k*m^2], AppendTo[a, n^2 + w*n*m + k*m^2]], {n, m, 400}], {m, 1, 400}]; Union[a] (*Artur Jasinski*)

A139509 Primes of the form x^2 + 29x*y + y^2 for x and y nonnegative.

Original entry on oeis.org

31, 97, 211, 373, 547, 607, 661, 769, 877, 1051, 1087, 1123, 1249, 1279, 1303, 1423, 1597, 1657, 1663, 1693, 1741, 1777, 1861, 1867, 2143, 2179, 2251, 2341, 2467, 2539, 2791, 2857, 3229, 3259, 3319, 3331, 3373, 3511, 3541, 3643, 3697, 3769, 3823, 3877
Offset: 1

Views

Author

Artur Jasinski, Apr 24 2008

Keywords

Links

Crossrefs

Cf. A139489, A007645, A068228, A007519, A033212, A033212, A107152, A107008, A033215, A107145, A139490, A139491.

Programs

  • Mathematica
    a = {}; w = 29; k = 1; Do[Do[If[PrimeQ[n^2 + w*n*m + k*m^2], AppendTo[a, n^2 + w*n*m + k*m^2]], {n, m, 400}], {m, 1, 400}]; Union[a] (*Artur Jasinski*)

A139510 Primes of the form x^2 + 30x*y + y^2 for x and y nonnegative.

Original entry on oeis.org

137, 193, 401, 617, 641, 953, 1009, 1129, 1289, 1297, 1801, 1913, 2129, 2137, 2377, 2473, 2657, 2713, 2801, 3049, 3257, 3313, 3329, 3593, 3889, 4001, 4057, 4153, 4201, 4337, 4649, 4657, 4729, 4817, 4937, 4993, 5009, 5153, 5209, 5441, 5657, 5849, 5881
Offset: 1

Views

Author

Artur Jasinski, Apr 24 2008

Keywords

Links

Crossrefs

Cf. A139489, A007645, A068228, A007519, A033212, A033212, A107152, A107008, A033215, A107145, A139490, A139491.

Programs

  • Mathematica
    a = {}; w = 30; k = 1; Do[Do[If[PrimeQ[n^2 + w*n*m + k*m^2], AppendTo[a, n^2 + w*n*m + k*m^2]], {n, m, 400}], {m, 1, 400}]; Union[a] (*Artur Jasinski*)

A139511 Primes of the form x^2 + 31x*y + y^2 for x and y nonnegative.

Original entry on oeis.org

67, 103, 181, 199, 223, 313, 397, 463, 487, 499, 631, 643, 661, 691, 709, 883, 991, 1021, 1039, 1093, 1153, 1213, 1321, 1483, 1543, 1567, 1741, 1747, 1753, 1831, 1879, 2017, 2029, 2083, 2113, 2137, 2179, 2203, 2269, 2311, 2377, 2539, 2557, 2677, 2731
Offset: 1

Views

Author

Artur Jasinski, Apr 24 2008

Keywords

Links

Crossrefs

Cf. A139489, A007645, A068228, A007519, A033212, A033212, A107152, A107008, A033215, A107145, A139490, A139491.

Programs

  • Mathematica
    a = {}; w = 31; k = 1; Do[Do[If[PrimeQ[n^2 + w*n*m + k*m^2], AppendTo[a, n^2 + w*n*m + k*m^2]], {n, m, 400}], {m, 1, 400}]; Union[a] (*Artur Jasinski*)

A141778 Primes of the form 4*x^2 + 3*x*y - 5*y^2 (as well as of the form 8*x^2 + 11*x*y + y^2).

Original entry on oeis.org

2, 5, 11, 17, 47, 53, 67, 71, 73, 79, 89, 97, 107, 109, 131, 139, 157, 167, 173, 179, 199, 223, 227, 233, 251, 257, 263, 269, 271, 277, 283, 307, 311, 317, 331, 347, 367, 373, 401, 409, 443, 449, 461, 463, 467, 479, 487, 509, 523, 587, 601, 607, 613, 619, 631
Offset: 1

Views

Author

Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (sergarmor(AT)yahoo.es), Jul 04 2008

Keywords

Comments

Discriminant = 89. Class = 1. Binary quadratic forms a*x^2+b*x*y+c*y^2 have discriminant d=b^2-4ac and gcd(a,b,c)=1.
A subsequence of (and may possibly coincide with) A038977. - R. J. Mathar, Jul 22 2008

Examples

			a(1) = 2 because we can write 2 = 4*1^2 + 3*1*1 - 5*1^2.

References

  • Z. I. Borevich and I. R. Shafarevich, Number Theory.

Links

Crossrefs

See also A038872 (d=5). A038873 (d=8). A068228, A141123 (d=12). A038883 (d=13). A038889 (d=17). A141158 (d=20). A141159, A141160 (d=21). A141170, A141171 (d=24). A141172, A141173 (d=28). A141174, A141175 (d=32). A141176, A141177 (d=33). A141178 (d=37). A141179, A141180 (d=40). A141181 (d=41). A141182, A141183 (d=44). A033212, A141785 (d=45). A068228, A141187 (d=48). A141188 (d=52). A141189 (d=53). A141190, A141191 (d=56). A141192, A141193 (d=57). A107152, A141302, A141303, A141304 (d=60). A141215 (d=61). A141111, A141112 (d=65). A141750 (d=73). A141772, A141773 (d=85). A141776, A141777 (d=88). A141778 (d=89). A141161, A141163 (d=148). A141165, A141166 (d=229). A141167, A141168 (d=257).

Extensions

Typo in crossrefs fixed by Colin Barker, Apr 05 2015
Previous Showing 31-40 of 41 results. Next

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