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 1-6 of 6 results.

A024974 Numbers that are the sum of 3 distinct positive cubes in 2 or more ways.

Original entry on oeis.org

1009, 1366, 1457, 1520, 1737, 1756, 1793, 1854, 1945, 2072, 2241, 2456, 2736, 3060, 3592, 3599, 3745, 3926, 4105, 4131, 4168, 4229, 4320, 4376, 4437, 4447, 4473, 4616, 4733, 4922, 5104, 5130, 5435, 5472, 5643, 5706, 5825, 5832, 6183, 6301, 6642, 6848
Offset: 1

Views

Author

Clark Kimberling

Keywords

Examples

			a(1) = 1009 = 1^3+2^3+10^3 = 4^3+6^3+9^3. - _Christian N. K. Anderson_, Apr 11 2013

Links

Crossrefs

Cf. A025400 (exactly 2 ways), A008917 (not necessarily distinct)

Formula

{n: A025469(n) >= 2}. - R. J. Mathar, Jun 15 2018

A180088 Primes which are the sum of three distinct positive cubes in two or more distinct ways.

Original entry on oeis.org

1009, 4229, 4447, 4733, 6301, 7561, 10657, 12377, 12979, 13103, 13859, 14561, 15569, 15667, 17207, 20663, 20747, 20899, 21673, 22511, 24137, 24499, 25999, 27793, 27917, 28001, 28493, 28729, 29917, 31123, 32579, 32833, 32957, 33119
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Aug 09 2010

Keywords

Comments

1^3+2^3+10^3=1009=4^3+6^3+9^3

Links

Crossrefs

Cf. A011541, A024974, A025400, A122723

Programs

  • Mathematica
    lst1=Sort@Select[Flatten[Table[a^3+b^3+c^3,{a,1,66},{b,a-1,1,-1},{c,b-1,1,-1}]],PrimeQ[ # ]&]; lst={};Do[If[lst1[[n]]==lst1[[n+1]],AppendTo[lst,lst1[[n]]]],{n,Length[lst1]-1}];lst

A374256 a(n) is the smallest number which can be represented as the sum of n distinct positive n-th powers in exactly 2 ways, or -1 if no such number exists.

Original entry on oeis.org

-1, 65, 1009, 6834, 1158224, 19198660, 1518471174, 301963223843, 14599274102522, 1601155487573222
Offset: 1

Views

Author

Ilya Gutkovskiy, Jul 01 2024

Keywords

Examples

			a(2) = 65 = 1^2 + 8^2 = 4^2 + 7^2.
a(3) = 1009 = 1^3 + 2^3 + 10^3 = 4^3 + 6^3 + 9^3.

Crossrefs

Cf. A025303, A025400, A091414, A146756, A374226, A374257.

Programs

  • Maple
    f:= proc(n) uses priqueue;
  local pq,w,t,g,i,count,newt;
  g:= proc(t) local i; [-add((t[i]+i)^n,i=1..n),op(t)] end proc;
  w:= [0$(n+1)];
  initialize(pq);
  insert(g([0$n]),pq);
  do
    t:= extract(pq);
    if t[1] = w[1] then return -t[1] fi;
    w:= t;
    for i from 2 to n+1 do
        if t[i]=t[-1] then
          newt:= g(t[2..-1] + [0$(i-2),1$(n+2-i)]);
        insert(newt,pq);
  fi od od;
end proc:
-1, seq(f(n),n=2..10); # Robert Israel, Jul 01 2024

Extensions

a(9)-a(10) from Robert Israel, Jul 01 2024

A180089 Semiprimes which are the sum of three distinct positive cubes in two or more distinct ways.

Original entry on oeis.org

1366, 1457, 1793, 1945, 3599, 4105, 5435, 7379, 8315, 9017, 10261, 10963, 11773, 12706, 13957, 15163, 15371, 15553, 15751, 15758, 16271, 17263, 17354, 17947, 18649, 19027, 19369, 19657, 19729, 19774, 19781, 19907, 21026, 21167, 22411
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Aug 09 2010

Keywords

Comments

2^3+3^3+11^3=5^3+8^3+9^3=1366=2*683, 1^3+5^3+11^3=6^3+8^3+9^3=1457=31*47,..

Links

Crossrefs

Cf. A011541, A024974, A025400, A122723, A180088

Programs

  • Mathematica
    f[n_]:=Last/@FactorInteger[n]=={1,1}; lst={};Do[Do[Do[If[f[p=a^3+b^3+c^3],AppendTo[lst,p]],{c,b-1,1,-1}],{b,a-1,1,-1}],{a,55}];lst1=Sort@lst; lst={};Do[If[lst1[[n]]==lst1[[n+1]],AppendTo[lst,lst1[[n]]]],{n,Length[lst1]-1}];lst

A180099 Primes which are the sum of three distinct positive cubes of prime numbers in two or more distinct ways.

Original entry on oeis.org

185527, 451837, 591751, 1265471, 1266929, 1618973, 1626227, 1664713, 2586277, 2754683, 2765519, 2805193, 3422303, 3740309, 3748499, 4154779, 5336479, 5483953, 5557987, 6130151, 6586091, 7231013, 7361801, 7726571, 8205553
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Aug 09 2010

Keywords

Examples

			185527 = 47^3+43^3+13^3=53^3+31^3+19^3.

Links

Crossrefs

Cf. A011541, A024974, A025400, A122723, A180088, A180089.

Programs

  • Mathematica
    lst={};Do[Do[Do[If[PrimeQ[p=Prime[a]^3+Prime[b]^3+Prime[c]^3],AppendTo[lst,p]],{c,b-1,1,-1}],{b,a-1,1,-1}],{a,88}];lst1=Sort@lst; lst={};Do[If[lst1[[n]]==lst1[[n+1]],AppendTo[lst,lst1[[n]]]],{n,Length[lst1]-1}];lst
Select[Tally[Select[Total/@Subsets[Prime[Range[50]]^3,{3}],PrimeQ]],#[[2]]> 1&] [[All,1]]//Sort (* Harvey P. Dale, Sep 26 2020 *)

A180106 Semiprimes which are the sum of three distinct positive cubes of semiprime numbers in two or more distinct ways.

Original entry on oeis.org

88073, 195905, 196057, 196841, 205102, 211466, 610903, 747209, 809966, 1078622, 1543267, 1828441, 1967402, 2143783, 2312029, 2803501, 3055258, 3108673, 3244466, 3477629, 3662567, 4237577, 4770137, 5741074, 5835593, 5908889, 7189265, 7497118, 8438249, 8742781
Offset: 1

Views

Author

Vladimir Joseph Stephan Orlovsky, Aug 10 2010

Keywords

Comments

610903 = 74^3+55^3+34^3 = 82^3+39^3+6^3.
88073 = 29*3037 = 21^3+33^3+35^3 = 25^3+26^3+38^3. - Chai Wah Wu, May 20 2017

Links

Crossrefs

Cf. A011541, A024974, A025400, A122723, A180088, A180089, A180099

Programs

  • Mathematica
    f[n_] := PrimeOmega@ n == 2; lst = {}; Do[Do[Do[If[And[f[a], f[b], f[c], f[p = a^3 + b^3 + c^3]], AppendTo[lst, p]], {c, b - 1, 1, -1}], {b, a - 1, 1, -1}], {a, 200}]; lst1 = Sort@ lst; lst = {}; Do[If[lst1[[n]] == lst1[[n + 1]], AppendTo[lst, lst1[[n]]]], {n, Length[lst1] - 1}]; lst (* Corrected by Michael De Vlieger, May 21 2017 *)

Extensions

Terms corrected by Chai Wah Wu, May 20 2017
Showing 1-6 of 6 results.

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