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 11-20 of 20 results.

A155574 Intersection of A154777 and A092572: N = a^2 + 2b^2 = c^2 + 3d^2 for some positive integers a,b,c,d.

Original entry on oeis.org

12, 19, 36, 43, 48, 57, 67, 73, 76, 97, 108, 129, 139, 144, 147, 163, 171, 172, 192, 193, 201, 211, 219, 228, 241, 268, 283, 291, 292, 300, 304, 307, 313, 324, 331, 337, 361, 379, 387, 388, 409, 417, 432, 433, 441, 457, 475, 484, 489, 499, 507, 513, 516, 523
Offset: 1

Views

Author

M. F. Hasler, Jan 25 2009

Keywords

Comments

Subsequence of A155564 (where a,b,c,d may be zero).

Crossrefs

Cf. A000404, A154777, A092572, A097268, A154778, A155716, A155717, A155560-A155578.

Programs

  • PARI
    isA155574(n,/* optional 2nd arg allows us to get other sequences */c=[3,2]) = { for(i=1,#c, for(b=1,sqrtint((n-1)\c[i]), issquare(n-c[i]*b^2) & next(2)); return);1}
for( n=1,999, isA155574(n) & print1(n","))

A155575 Intersection of A000404 and A154778: N = a^2 + b^2 = c^2 + 5d^2 for some positive integers a,b,c,d.

Original entry on oeis.org

29, 41, 45, 61, 89, 101, 109, 116, 145, 149, 164, 180, 181, 205, 225, 229, 241, 244, 245, 261, 269, 281, 305, 349, 356, 369, 389, 401, 404, 405, 409, 421, 436, 445, 449, 461, 464, 505, 509, 521, 541, 545, 549, 569, 580, 596, 601, 641, 656, 661, 701, 709, 720
Offset: 1

Views

Author

M. F. Hasler, Jan 25 2009

Keywords

Comments

Subsequence of A155565 (where a,b,c,d may be zero).

Crossrefs

Cf. A000404, A154777, A092572, A097268, A154778, A155716, A155717, A155560-A155578.

Programs

  • PARI
    isA155575(n,/* optional 2nd arg allows us to get other sequences */c=[5,1]) = { for(i=1,#c, for(b=1,sqrtint((n-1)\c[i]), issquare(n-c[i]*b^2) & next(2)); return);1}
for( n=1,999, isA155575(n) & print1(n","))

A155577 Intersection of A154777 and A154778: N = a^2 + 2b^2 = c^2 + 5d^2 for some positive integers a,b,c,d.

Original entry on oeis.org

6, 9, 24, 36, 41, 54, 81, 86, 89, 96, 129, 134, 144, 150, 164, 166, 201, 214, 216, 225, 241, 246, 249, 281, 294, 321, 324, 326, 344, 356, 369, 384, 401, 409, 441, 449, 454, 486, 489, 516, 521, 534, 536, 566, 569, 576, 600, 601, 614, 641, 656, 664, 681, 694
Offset: 1

Views

Author

M. F. Hasler, Jan 25 2009

Keywords

Comments

Subsequence of A155567 (where a,b,c,d may be zero).

Crossrefs

Cf. A000404, A154777, A092572, A097268, A154778, A155716, ...

Programs

  • PARI
    isA155577(n,/* optional 2nd arg allows us to get other sequences */c=[5,2]) = { for(i=1,#c, for(b=1,sqrtint((n-1)\c[i]), issquare(n-c[i]*b^2) & next(2)); return);1}
for( n=1,999, isA155577(n) & print1(n","))

A155710 Intersection of A092572 and A154778: N = a^2 + 3b^2 = c^2 + 5d^2 for some positive integers a,b,c,d.

Original entry on oeis.org

21, 36, 49, 61, 84, 109, 129, 144, 181, 189, 196, 201, 229, 241, 244, 301, 309, 324, 336, 349, 381, 409, 421, 436, 441, 469, 489, 516, 525, 541, 549, 576, 601, 661, 669, 709, 721, 724, 756, 769, 784, 804, 829, 849, 889, 900, 916, 921, 964, 976, 981, 1009, 1021
Offset: 1

Views

Author

M. F. Hasler, Jan 25 2009

Keywords

Comments

Subsequence of A155570 (where a,b,c,d may be zero).

Crossrefs

Cf. A000404, A154777, A092572, A097268, A154778, A155716, ...

Programs

  • PARI
    isA155710(n,/* use optional 2nd arg to get other analogous sequences */c=[5,3]) = { for(i=1,#c, for(b=1,sqrtint((n-1)\c[i]), issquare(n-c[i]*b^2) & next(2)); return);1}
for( n=1,1111, isA155710(n) & print1(n","))

A155571 Intersection of A000404, A092572 and A154778: N = a^2 + b^2 = c^2 + 3d^2 = e^2 + 5f^2 for some positive integers a,b,c,d,e,f.

Original entry on oeis.org

61, 109, 181, 229, 241, 244, 349, 409, 421, 436, 541, 549, 601, 661, 709, 724, 769, 829, 900, 916, 964, 976, 981, 1009, 1021, 1069, 1129, 1201, 1225, 1249, 1321, 1381, 1396, 1429, 1489, 1521, 1525, 1549, 1609, 1621, 1629, 1636, 1669, 1684, 1741, 1744, 1789
Offset: 1

Views

Author

M. F. Hasler, Jan 25 2009

Keywords

Crossrefs

Cf. A000404, A154777, A092572, A097268, A154778, A155716, A155717, A155560-A155578.

Programs

  • PARI
    isA155571(n,/* optional 2nd arg allows us to get other sequences */c=[5,3,1]) = { for(i=1,#c, for(b=1,sqrtint((n-1)\c[i]), issquare(n-c[i]*b^2) & next(2)); return);1}
for( n=1,1999, isA155571(n) & print1(n","))

A155572 Intersection of A000404, A154777 and A154778: N = a^2 + b^2 = c^2 + 2d^2 = e^2 + 5f^2 for some positive integers a,b,c,d,e,f.

Original entry on oeis.org

41, 89, 164, 225, 241, 281, 356, 369, 401, 409, 449, 521, 569, 601, 641, 656, 761, 769, 801, 809, 881, 900, 929, 964, 1009, 1025, 1049, 1124, 1129, 1201, 1249, 1289, 1321, 1361, 1409, 1424, 1476, 1481, 1489, 1521, 1601, 1604, 1609, 1636, 1681, 1721, 1796
Offset: 1

Views

Author

M. F. Hasler, Jan 25 2009

Keywords

Crossrefs

Cf. A000404, A154777, A092572, A097268, A154778, A155716, A155717, A155560-A155578.

Programs

  • PARI
    isA155572(n,/* optional 2nd arg allows us to get other sequences */c=[5,2,1]) = { for(i=1,#c, for(b=1,sqrtint((n-1)\c[i]), issquare(n-c[i]*b^2) & next(2)); return);1}
for( n=1,1999, isA155572(n) & print1(n","))

A155573 Intersection of A000404, A154777 and A092572: N = a^2 + b^2 = c^2 + 2d^2 = e^2 + 3f^2 for some positive integers a,b,c,d,e,f.

Original entry on oeis.org

73, 97, 193, 241, 292, 313, 337, 388, 409, 433, 457, 577, 601, 657, 673, 769, 772, 873, 900, 937, 964, 1009, 1033, 1129, 1153, 1156, 1168, 1201, 1249, 1252, 1297, 1321, 1348, 1489, 1521, 1552, 1609, 1636, 1657, 1732, 1737, 1753, 1777, 1801, 1825, 1828
Offset: 1

Views

Author

M. F. Hasler, Jan 25 2009

Keywords

Crossrefs

Cf. A000404, A154777, A092572, A097268, A154778, A155716, A155717, A155560-A155578.

Programs

  • PARI
    isA155573(n,/* optional 2nd arg allows us to get other sequences */c=[3,2,1]) = { for(i=1,#c, for(b=1,sqrtint((n-1)\c[i]), issquare(n-c[i]*b^2) & next(2)); return);1}
for( n=1,1999, isA155573(n) & print1(n","))

A155711 Intersection of A154777 and A155717: N = a^2 + 2b^2 = c^2 + 7d^2 for some positive integers a,b,c,d.

Original entry on oeis.org

11, 43, 44, 67, 72, 88, 99, 107, 113, 121, 137, 144, 163, 172, 176, 179, 193, 211, 233, 268, 275, 281, 288, 331, 337, 344, 347, 352, 379, 387, 396, 401, 428, 443, 449, 452, 457, 473, 484, 491, 499, 536, 539, 547, 548, 569, 571, 576, 603, 617, 641, 648, 652
Offset: 1

Views

Author

M. F. Hasler, Jan 25 2009

Keywords

Crossrefs

Cf. A000404, A154777, A092572, A097268, A154778, A155716, A155717, A155560-A155578.

Programs

  • PARI
    isA155711(n,/* optional 2nd arg allows us to get other sequences */c=[7,2]) = { for(i=1,#c, for(b=1,sqrtint((n-1)\c[i]), issquare(n-c[i]*b^2) & next(2)); return);1}
for( n=1,999, isA155711(n) & print1(n","))

A216510 Number of positive integer solutions to the equation a^2 + 6*b^2 = n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1
Offset: 1

Views

Author

V. Raman, Sep 08 2012

Keywords

Crossrefs

Cf. A155716.

A216569 Numbers n such that the n-th Fibonacci number is prime and can be written in the form a^2 + 6*b^2.

Original entry on oeis.org

23, 47, 359, 431, 433, 9311, 25561, 35999, 37511, 50833, 81839, 590041, 593689, 1285607, 1636007, 1968721
Offset: 1

Views

Author

V. Raman, Sep 08 2012

Keywords

Links

Crossrefs

Cf. A000045, A001605.
Intersection of A005478 and A155716.

Programs

  • Mathematica
    Select[Range[2*10^6],PrimeQ[Fibonacci[#]]&&FindInstance[a^2+6b^2==Fibonacci[#],{a,b},Integers]!={}&] (* Harvey P. Dale, Sep 18 2019 *)
Previous Showing 11-20 of 20 results.

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