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 21-30 of 41 results. Next

A106861 Primes of the form x^2+xy+4y^2, with x and y nonnegative.

Original entry on oeis.org

19, 31, 79, 109, 151, 181, 199, 211, 229, 271, 331, 349, 409, 421, 439, 499, 571, 601, 619, 631, 661, 691, 709, 769, 811, 829, 859, 919, 991, 1021, 1039, 1051, 1069, 1129, 1171, 1201, 1249, 1291, 1321, 1381, 1399, 1429, 1459, 1471, 1489, 1531, 1579
Offset: 1

Views

Author

T. D. Noe, May 09 2005

Keywords

Comments

Discriminant=-15.
Subset of A033212. - Robert Israel, Jul 25 2014

Links

Crossrefs

Cf. A033212.

Programs

  • Maple
    N:= 1000; # to get all terms <= N
Primes:= select(isprime,[seq(2*n+1,n=1..floor((N-1)/2))]):
filter:= proc(p) local S;
  S:= remove(hastype,[isolve(x^2+x*y+4*y^2=p)],negint);
  nops(S) > 0
end proc:
A:= select(filter,Primes); # Robert Israel, Jul 25 2014
  • Mathematica
    QuadPrimes2[1, 1, 4, 1000000] (* see A106856 *)

A139505 Primes of the form x^2 + 25x*y + y^2 for x and y nonnegative.

Original entry on oeis.org

151, 163, 307, 397, 409, 541, 547, 601, 673, 811, 823, 859, 967, 997, 1153, 1231, 1237, 1327, 1567, 1669, 1741, 1879, 2083, 2143, 2281, 2293, 2557, 2677, 2707, 2833, 2971, 3037, 3259, 3313, 3433, 3877, 4003, 4129, 4153, 4603, 4639, 4861, 4957, 5101, 5227
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 = 25; 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=80},Select[Union[#[[1]]^2+25#[[1]]#[[2]]+#[[2]]^2&/@Tuples[ Range[ 0,nn],2]],PrimeQ[#]&&#Harvey P. Dale, Feb 10 2020 *)

A141750 Primes of the form 4*x^2 + 3*x*y - 4*y^2 (as well as of the form 2*x^2 + 9*x*y + y^2).

Original entry on oeis.org

2, 3, 19, 23, 37, 41, 61, 67, 71, 73, 79, 89, 97, 109, 127, 137, 149, 173, 181, 211, 223, 227, 251, 257, 269, 283, 293, 311, 317, 347, 349, 353, 359, 367, 373, 383, 389, 397, 401, 419, 439, 457, 461, 463, 479, 487, 499, 503, 509, 523, 547, 557, 587, 593, 607
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 03 2008

Keywords

Comments

Discriminant = 73. Class = 1. Binary quadratic forms a*x^2 + b*x*y + c*y^2 have discriminant d = b^2-4ac.
Is this the same as A038957? - R. J. Mathar, Jul 04 2008. Answer: almost certainly - see the Tunnell notes in A033212. - N. J. A. Sloane, Oct 18 2014

Examples

			a(2) = 3 because we can write 3 = 4*1^2 + 3*1*1 - 4*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). A141161, A141163 (d=148). A141165, A141166 (d=229). A141167, A141168 (d=257).

A141772 Primes of the form 3*x^2 + 5*x*y - 5*y^2 (as well as of the form 7*x^2 + 13*x*y + 3*y^2).

Original entry on oeis.org

3, 5, 7, 17, 23, 37, 73, 97, 107, 113, 163, 167, 173, 193, 197, 227, 233, 277, 283, 313, 317, 337, 347, 367, 397, 487, 503, 547, 607, 617, 643, 653, 673, 677, 683, 743, 787, 823, 827, 853, 857, 877, 887, 907, 947, 983, 997, 1013, 1093, 1117, 1153, 1163, 1187
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 = 85. Class = 2. Binary quadratic forms a*x^2 + b*x*y + c*y^2 have discriminant d = b^2 - 4ac.

Examples

			a(1) = 3 because we can write 3 = 3*1^2 + 5*1*0 - 5*0^2 (or 3 = 7*0^2 + 13*0*1 + 3*1^2).

References

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

Links

Crossrefs

Cf. A141773 (d=85). 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). A141161, A141163 (d=148). A141165, A141166 (d=229). A141167, A141168 (d=257).

Extensions

More terms from Colin Barker, Apr 04 2015
Typo in crossrefs fixed by Colin Barker, Apr 05 2015

A139493 Primes of the form x^2 + 9x*y + y^2 for x and y nonnegative.

Original entry on oeis.org

11, 23, 37, 53, 67, 71, 113, 137, 163, 179, 191, 317, 331, 379, 389, 401, 421, 443, 449, 463, 487, 499, 599, 617, 631, 641, 653, 683, 709, 751, 757, 823, 863, 883, 907, 911, 947, 977, 991, 1061, 1087, 1093, 1103, 1171, 1213, 1303, 1367, 1373, 1409, 1423
Offset: 1

Views

Author

Artur Jasinski, Apr 24 2008

Keywords

Comments

This is a member of the family of sequences of primes of the forms x^2 + kxy + y^2.
See for k=1 A007645 = x^2+3y^2, k=2 squares no primes, k=3 A038872, k=4 A068228 = x^2+9y^2, k=5 A139492, k=6 A007519 = x^2+8y^2, k=7 A033212 = x^2+15y^2, k=8 A107152 = x^2+45y^2, k=9 A139493, k=10 A107008 = x^2+24y^2, k=11 A139494, k=12 A139495, k=13 A139496, k=14* = 10 A107008 = x^2+24y^2, k=15 A139497, k=16 A033215 = x^2+21y^2, k=17 A139498, k=18 A107145 = x^2+40y^2, k=19 A139499, k=20 A139500, k=21 A139501, k=22 A139502, k=23 A139503, k=24 A139504, k=25 A139505, k=26,A139506, k=27 A139507, k=28 A139508, k=29 A139509, k=30 A139510, k=31 A139511, k=32 A139512

Links

Crossrefs

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

Programs

  • Mathematica
    a = {}; w = 9; 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*)

A139495 Primes of the form x^2 + 12x*y + y^2 for x and y nonnegative.

Original entry on oeis.org

29, 109, 149, 281, 389, 401, 421, 449, 541, 569, 641, 701, 709, 809, 821, 1009, 1061, 1129, 1201, 1229, 1289, 1381, 1409, 1429, 1481, 1549, 1621, 1709, 1789, 1801, 1901, 2069, 2081, 2129, 2221, 2269, 2381, 2389, 2521, 2549, 2689, 2741, 2801, 2909, 2969
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 = 12; 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[Union[Select[#[[1]]^2+12#[[1]]#[[2]]+#[[2]]^2&/@ Tuples[ Range[ nn],2],PrimeQ]],nn]] (* Harvey P. Dale, Dec 18 2015 *)

A139496 Primes of the form x^2 + 13x*y + y^2 for x and y nonnegative.

Original entry on oeis.org

31, 181, 199, 229, 331, 379, 421, 499, 619, 631, 661, 691, 709, 751, 829, 859, 991, 1021, 1039, 1171, 1279, 1291, 1321, 1489, 1549, 1609, 1621, 1699, 1741, 1831, 1879, 1951, 2011, 2029, 2161, 2179, 2269, 2281, 2311, 2341, 2539, 2671, 2689, 2731, 2971
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 = 13; 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*)

A139497 Primes of the form x^2 + 15x*y + y^2 for x and y nonnegative.

Original entry on oeis.org

17, 101, 103, 127, 179, 251, 263, 373, 433, 563, 599, 647, 701, 757, 797, 937, 953, 971, 1063, 1069, 1223, 1277, 1427, 1453, 1481, 1483, 1531, 1543, 1583, 1667, 1699, 1759, 1811, 1871, 2053, 2083, 2089, 2141, 2297, 2393, 2473, 2549, 2837, 2843, 2909, 2939
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 = 15; 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*)

A139498 Primes of the form x^2 + 17x*y + y^2 for x and y nonnegative.

Original entry on oeis.org

19, 61, 139, 199, 229, 271, 349, 499, 541, 571, 619, 631, 691, 709, 739, 769, 859, 919, 1051, 1069, 1201, 1279, 1429, 1489, 1531, 1621, 1669, 1759, 1831, 1879, 1999, 2011, 2221, 2239, 2251, 2281, 2341, 2551, 2671, 2791, 2851, 2971, 3019, 3049, 3079, 3121
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 = 17; 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*)

A139499 Primes of the form x^2 + 19x*y + y^2 for x and y nonnegative.

Original entry on oeis.org

43, 67, 127, 151, 331, 373, 421, 457, 463, 613, 631, 739, 757, 883, 919, 967, 1033, 1087, 1171, 1327, 1381, 1429, 1453, 1471, 1549, 1579, 1597, 1747, 1759, 1789, 1801, 2053, 2083, 2143, 2269, 2293, 2311, 2347, 2389, 2473, 2503, 2671, 2767, 2797, 2857
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 = 19; 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*)
upto=3000;With[{max=Ceiling[Sqrt[upto]]},Select[Union[Select[(First[#]^2+ 19First[#]Last[#]+ Last[#]^2)&/@(Tuples[Range[0,max],{2}]), PrimeQ]], #<+upto&]] (* Harvey P. Dale, Jul 20 2011 *)
Previous Showing 21-30 of 41 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.