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 1-7 of 7 results.

A124966 Numbers which can be expressed as the ordered sum of 3 squares in 2 or more different ways.

Original entry on oeis.org

9, 17, 18, 25, 26, 27, 29, 33, 34, 36, 38, 41, 45, 49, 50, 51, 53, 54, 57, 59, 61, 62, 65, 66, 68, 69, 72, 73, 74, 75, 77, 81, 82, 83, 85, 86, 89, 90, 94, 97, 98, 99, 100, 101, 102, 104, 105, 106, 107, 108, 109, 110, 113, 114, 116, 117, 118, 121, 122, 123, 125, 126, 129
Offset: 1

Views

Author

Artur Jasinski, Nov 14 2006

Keywords

Examples

			a(1)=9 because 9 = 3^2 + 0^2 + 0^2 or 2^2 + 2^2 + 1^2.

Links

Crossrefs

Cf. A004215, A094942, A124967-A124971.

Programs

  • Mathematica
    Select[Range[129], Length@PowersRepresentations[#, 3, 2] >= 2 &] (* Ray Chandler, Oct 31 2019 *)

Formula

Equals = A000027 - A094942 - A004215.

Extensions

Corrected and extended by Ray Chandler, Nov 30 2006

A124968 Numbers which can be expressed as the ordered sum of 3 squares in 4 or more different ways.

Original entry on oeis.org

81, 89, 101, 125, 129, 134, 146, 149, 153, 161, 162, 170, 171, 173, 185, 189, 194, 198, 201, 206, 209, 221, 225, 230, 233, 234, 241, 242, 243, 245, 246, 249, 250, 251, 254, 257, 261, 266, 269, 270, 274, 278, 281, 285, 289, 290, 293, 294, 297, 299, 305, 306
Offset: 1

Views

Author

Artur Jasinski, Nov 14 2006

Keywords

Comments

Subset of A124967.

Examples

			a(1)=81 because 81 = 6^2 + 6^2 + 3^2 = 7^2 + 4^2 + 4^2 = 8^2 + 4^2 + 1^2 = 9^2 + 0^2 + 0^2.
161 = 1^2 + 4^2 + 12^2 = 2^2 + 6^2 + 11^2 = 4^2 + 8^2 + 9^2 = 5^2 + 6^2 + 10^2, so 161 is in the list.

Links

Crossrefs

Cf. A124966-A124971.

Programs

  • Mathematica
    Select[Range[310], Length@PowersRepresentations[#, 3, 2] >= 4 &] (* Ray Chandler, Oct 31 2019 *)
  • PARI
    isA124968(n)={ local(cnt=0,z2) ; for(x=0,floor(sqrt(n)), for(y=x,floor(sqrt(n-x^2)), z2=n-x^2-y^2 ; if( z2>=y^2 && issquare(z2), cnt++ ; ) ; if(cnt >=4, return(1) ) ; ) ; ) ; return(0) ; } { for(n=1,800, if( isA124968(n), print1(n,", ") ; ) ; ) ; } \\ R. J. Mathar

Extensions

Corrected and extended by Ray Chandler and R. J. Mathar, Nov 29 2006

A294578 Numbers which can be expressed as an ordered sum of 3 squares in 6 or more different ways.

Original entry on oeis.org

194, 209, 269, 281, 290, 297, 306, 314, 321, 326, 329, 341, 342, 365, 369, 374, 386, 389, 401, 425, 426, 434, 441, 446, 449, 450, 458, 459, 461, 482, 485, 486, 489, 494, 497, 506, 509, 513, 521, 530, 531, 534, 542, 545, 546, 549, 554, 558, 561, 566, 569, 578
Offset: 1

Views

Author

Robert Price, Nov 02 2017

Keywords

Links

Crossrefs

Cf. A000164, A094942, A124966, A124967, A124968.

Programs

  • Mathematica
    Select[Range[578], Length[PowersRepresentations[#, 3, 2]] >= 6 &]

Extensions

Updated Mathematica program to Version 11. by Robert Price, Nov 01 2019

A294596 Numbers which can be expressed as an ordered sum of 3 squares in 7 or more different ways.

Original entry on oeis.org

306, 314, 341, 369, 374, 425, 441, 446, 450, 458, 461, 486, 494, 506, 509, 521, 530, 545, 549, 566, 569, 581, 585, 593, 594, 605, 614, 621, 626, 629, 641, 650, 654, 657, 666, 674, 677, 686, 689, 698, 701, 706, 710, 725, 726, 729, 731, 734, 738, 746, 749, 761
Offset: 1

Views

Author

Robert Price, Nov 03 2017

Keywords

Links

Crossrefs

Cf. A000164, A094942, A124966, A124967, A124968, A124969, A294578.

Programs

  • Mathematica
    Select[Range[761], Length[PowersRepresentations[#, 3, 2]] >= 7 &]

Extensions

Updated Mathematica program to Version 11. by Robert Price, Nov 01 2019

A294597 Numbers which can be expressed as an ordered sum of 3 squares in 8 or more different ways.

Original entry on oeis.org

369, 374, 425, 446, 461, 486, 509, 521, 530, 545, 549, 566, 569, 594, 614, 621, 626, 629, 641, 650, 666, 677, 686, 689, 701, 710, 725, 729, 734, 749, 761, 770, 774, 789, 794, 797, 801, 809, 810, 818, 821, 825, 833, 845, 846, 849, 854, 857, 866, 869, 881, 882
Offset: 1

Views

Author

Robert Price, Nov 03 2017

Keywords

Links

Crossrefs

Cf. A000164, A094942, A124966, A124967, A124968.

Programs

  • Mathematica
    Select[Range[1000],Length[PowersRepresentations[#,3,2]]>7&] (* Harvey P. Dale, Jul 03 2019 *)

A294714 Numbers which can be expressed as an ordered sum of 3 squares in 9 or more different ways.

Original entry on oeis.org

425, 521, 545, 569, 594, 614, 626, 629, 650, 689, 701, 725, 729, 734, 761, 774, 794, 801, 809, 810, 845, 846, 854, 857, 866, 881, 909, 914, 926, 929, 941, 950, 953, 965, 974, 986, 989, 990, 1001, 1025, 1026, 1034, 1041, 1046, 1049, 1053, 1062, 1070, 1074
Offset: 1

Views

Author

Robert Price, Nov 07 2017

Keywords

Links

Crossrefs

Cf. A000164, A094942, A124966, A124967, A124968.

Programs

  • Mathematica
    Select[Range[882], Length[PowersRepresentations[#, 3, 2]] >= 9 &]

Extensions

Updated Mathematica program to Version 11. by Robert Price, Nov 01 2019

A294715 Numbers which can be expressed as an ordered sum of 3 squares in 10 or more different ways.

Original entry on oeis.org

594, 626, 629, 689, 734, 761, 794, 801, 846, 854, 866, 881, 909, 914, 926, 929, 941, 950, 965, 986, 1001, 1025, 1026, 1034, 1041, 1046, 1049, 1089, 1097, 1106, 1109, 1121, 1125, 1130, 1154, 1161, 1169, 1181, 1190, 1193, 1205, 1206, 1209, 1214, 1226, 1229
Offset: 1

Views

Author

Robert Price, Nov 07 2017

Keywords

Crossrefs

Cf. A000164, A094942, A124966, A124967, A124968.

Programs

  • Mathematica
    Select[Range[1229], Length[PowersRepresentations[#, 3, 2]] >= 10 &]

Extensions

Updated Mathematica program to Version 11, and corrected errors in Name. by Robert Price, Nov 01 2019
Showing 1-7 of 7 results.

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