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.

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A374418 a(n) is the smallest number which can be represented as the sum of 2 distinct positive n-th powers in exactly 3 ways, or -1 if no such number exists.

Original entry on oeis.org

7, 325, 87539319
Offset: 1

Views

Author

Ilya Gutkovskiy, Jul 08 2024

Keywords

Comments

See also comments in A338799.

Examples

			a(2) = 325 = 1^2 + 18^2 = 6^2 + 17^2 = 10^2 + 15^2.
a(3) = 87539319 = 167^3 + 436^3 = 228^3 + 423^3 = 255^3 + 414^3.
		

Crossrefs

A338800 Smallest number that is the sum of two distinct n-th powers of primes in two different ways.

Original entry on oeis.org

16, 410, 6058655748, 3262811042
Offset: 1

Views

Author

Ilya Gutkovskiy, Nov 10 2020

Keywords

Comments

The Lander, Parkin, and Selfridge conjecture implies that for n >= 5 a number can be the sum of two n-th powers of positive integers in at most one way, and in particular that a(n) does not exist for n >= 5. - Robert Israel, Nov 13 2020
a(5) > 10^31 if it exists. - Michael S. Branicky, Jul 01 2024

Examples

			16 = 3 + 13 = 5 + 11.
410 = 7^2 + 19^2 = 11^2 + 17^2.
6058655748 = 61^3 + 1823^3 = 1049^3 + 1699^3.
3262811042 = 7^4 + 239^4 = 157^4 + 227^4.
		

Crossrefs

Programs

  • Maple
    f:= proc(n) local S,P,p,pn,b;
      S:= {}:
      P:= {}:
      p:= 1:
      b:= infinity;
      do
       p:= nextprime(p);
       pn:= p^n;
       if pn > b then return b fi;
       V:= select(`<`,map(`+`,P,pn),b);
       newv:= V intersect S;
       S:= S union V;
       P:= P union {p^n};
       if newv <> {} then
         b:= min(newv);
         S:= select(`<`,S,b);
         P:= select(`<`,P, b);
       fi;
      od:
    end proc:
    map(f, [$1..4]); # Robert Israel, Nov 13 2020
Showing 1-2 of 2 results.