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 1-5 of 5 results.

A102619 Numbers which are the sum of two positive cubes and divisible by 19.

Original entry on oeis.org

133, 152, 513, 855, 1064, 1216, 1729, 1843, 2071, 2261, 2413, 2869, 2926, 3059, 3439, 3591, 4104, 4123, 4921, 4940, 5833, 6175, 6840, 7163, 7657, 8512, 9386, 9728, 10773, 13167, 13357, 13718, 13832, 13851, 14174, 14364, 14744, 15542, 15561, 16568
Offset: 1

Views

Author

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Jan 31 2005

Keywords

Comments

If 12*h-1083 is a square then some values of 19*h are in this sequence. It is easy to verify that h is of the form 3*m^2-3*m+91, and therefore 19*(3*m^2-3*m+91) = (10-m)^3+(m+9)^3. - Vincenzo Librandi, May 10 2013

Links

Crossrefs

Cf. A003325, A101421 (divisible by k=7), A101852 (k=11), A094447 (k=13), A099178 (k=17), A101806 (k=23), A224483 (k=29), A102658 (k=31), A102618 (k=37).

Programs

  • Magma
    [n: n in [2..2*10^4] | exists{i: i in [1..Iroot(n-1,3)] | IsPower(n-i^3,3) and IsZero(n mod 19)}]; // Bruno Berselli, May 10 2013
  • Mathematica
    upto[n_] := Block[{t}, Union@ Reap[ Do[If[ Mod[t = x^3 + y^3, 19] == 0, Sow@t], {x, n^(1/3)}, {y, Min[x, (n - x^3)^(1/3)]}]][[2, 1]]]; upto[17000] (* Giovanni Resta, Jun 12 2020 *)

A102658 Numbers which are the sum of two positive cubes and divisible by 31.

Original entry on oeis.org

217, 341, 1395, 1674, 1736, 2728, 4123, 5425, 5642, 5859, 6293, 7471, 7657, 8029, 8587, 9207, 9269, 9331, 10261, 11160, 11377, 12679, 12896, 13392, 13888, 14167, 14911, 15841, 16120, 17577, 17701, 19747, 20026, 21824, 21979, 24149, 24397
Offset: 1

Views

Author

Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Feb 02 2005

Keywords

Links

Crossrefs

Cf. A003325, A101421 (divisible by k=7), A101852 (k=11), A094447 (k=13), A099178 (k=17), A102619 (k=19), A101806 (k=23), A224483 (k=29), A102618 (k=37).

Programs

  • Mathematica
    upto[n_] := Block[{t}, Union@ Reap[ Do[If[Mod[t = x^3 + y^3, 31] == 0, Sow@t], {x, n^(1/3)}, {y, Min[x, (n - x^3)^(1/3)]}]][[2, 1]]]; upto[24500] (* Giovanni Resta, Jun 12 2020 *)

A224483 Numbers which are the sum of two positive cubes and divisible by 29.

Original entry on oeis.org

6119, 6293, 6641, 7163, 7859, 8729, 9773, 10991, 12383, 13949, 15689, 17603, 19691, 21953, 48778, 48952, 49474, 50344, 51562, 53128, 55042, 57304, 59914, 62872, 66178, 69832, 73834, 78184, 82882, 87928, 93322, 99064, 105154
Offset: 1

Views

Author

Vincenzo Librandi, May 08 2013

Keywords

Comments

If 12*h-2523 is a square then some values of 29*h are in this sequence.
It is easy to verify that h is of the form 3*m^2-9*m+217, and therefore 29*(3*m^2-9*m+217) = (16-m)^3+(m+13)^3. [Bruno Berselli, May 10 2013]

Links

Crossrefs

Cf. numbers which are the sum of two positive cubes and divisible by k: A101421 (k=7), A101852 (k=11), A094447 (k=13), A099178 (k=17), A102619 (k=19), A101806 (k=23), A102658 (k=31), A102618 (k=37).

Programs

  • Magma
    [n: n in [2..2*10^5] | exists{i: i in [1..Iroot(n-1,3)] | IsPower(n-i^3,3) and IsZero(n mod 29)}]; // Bruno Berselli, May 10 2013
  • Mathematica
    upto[n_] := Block[{t}, Union@Reap[ Do[If[Mod[t = x^3 + y^3, 29] == 0, Sow@t], {x, n^(1/3)}, {y, Min[x, (n - x^3)^(1/3)]}]][[2, 1]]]; upto[106000] (* Giovanni Resta, Jun 12 2020 *)

A224484 Numbers which are the sum of two positive cubes and divisible by 3.

Original entry on oeis.org

9, 54, 72, 126, 189, 243, 351, 432, 468, 513, 576, 756, 855, 945, 1008, 1125, 1332, 1395, 1458, 1512, 1674, 1755, 1944, 2205, 2322, 2331, 2457, 2709, 2745, 2808, 3087, 3402, 3456, 3528, 3591, 3744, 4104, 4221, 4608, 4914, 4941
Offset: 1

Views

Author

Vincenzo Librandi, May 10 2013

Keywords

Comments

If 12*h-27 is a square then some values of 3*h are in this sequence. It is easy to verify that h is of the form 3*m^2-3*m+3, and therefore 9*(m^2-m+1) = (2-m)^3+(m+1)^3.
All entries are multiples of 9. [Proof: the cubes mod 3 are A010872. So the two cubes are either of the form (3i)^3 and (3j)^3 or (3i+1)^3 and (3j+2)^3. The same 3-periodic pattern is seen in the cubes modulo 9, A167176.] - R. J. Mathar, Aug 24 2016

Links

Crossrefs

Cf. A224485 (divisible by k=5), A101421 (k=7), A101852 (k=11), A094447 (k=13), A099178 (k=17), A102619 (k=19), A101806 (k=23), A224483 (k=29), A102658 (k=31), A102618 (k=37).

Programs

  • Mathematica
    upto[n_] := Block[{t}, Union@ Reap[ Do[If[Mod[t = x^3 + y^3, 3] == 0, Sow@ t], {x, n^(1/3)}, {y, Min[x, (n - x^3)^(1/3)]}] ][[2, 1]]]; upto[5000] (* Giovanni Resta, Jun 12 2020 *)
Module[{nn=20},Select[Union[Total/@Tuples[Range[nn]^3,2]],Mod[#,3]==0 && #Harvey P. Dale, Mar 06 2022 *)

A224485 Numbers which are the sum of two positive cubes and divisible by 5.

Original entry on oeis.org

35, 65, 250, 280, 370, 520, 730, 855, 945, 1125, 1395, 1755, 2000, 2060, 2205, 2240, 2540, 2745, 2960, 3500, 3925, 4075, 4160, 4375, 4825, 4940, 5425, 5840, 6175, 6750, 6840, 6860, 7075, 7110, 7560, 8125, 8190, 9000, 9325, 9990
Offset: 1

Views

Author

Vincenzo Librandi, May 10 2013

Keywords

Comments

If 12*h-75 is a square then some values of 5*h are in this sequence. It is easy to verify that h is of the form 3*m^2-3*m+7, and therefore 5*(3*m^2-3*m+7) = (3-m)^3+(m+2)^3.

Links

Crossrefs

Cf. A224484 (divisible by k=3), A101421 (k=7), A101852 (k=11), A094447 (k=13), A099178 (k=17), A102619 (k=19), A101806 (k=23), A224483 (k=29), A102658 (k=31), A102618 (k=37).

Programs

  • Mathematica
    upto[n_] := Block[{t}, Union@ Reap[ Do[If[Mod[t = x^3 + y^3, 5] == 0, Sow@t], {x, n^(1/3)}, {y, Min[x, (n - x^3)^(1/3)]}]][[2, 1]]]; upto[10000] (* Giovanni Resta, Jun 12 2020 *)
Showing 1-5 of 5 results.

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