OFFSET
1,3
COMMENTS
Is there a solution n such that n^n = (x^3 + y^3) / 2 where x > y > 0?
The answer to the above question is yes: 76^76 = (523974089123227128080087214816032969930445946880^3 + 314384453473936276848052328889619781958267568128^3)/2. Other examples include 112^112 and 172^172. - Chai Wah Wu, Jan 18 2016
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..228
EXAMPLE
1 is a term because 1^1 = 1 = (1^3 + 1^3) / 2.
3 is a term because 3^3 = 27 = (3^3 + 3^3) / 2.
8 is a term because 8^8 = 2^24 = (256^3 + 256^3) / 2.
MATHEMATICA
Select[Range@ 24, Resolve[Exists[{x, y}, And[Reduce[#^# == (x^3 + y^3)/2, {x, y}, Integers], x > 0, y > 0]]] &] (* Michael De Vlieger, Jan 15 2016 *)
PROG
(PARI) T=thueinit('z^3+1);
is(n) = #select(v->min(v[1], v[2])>0, thue(T, n))>0;
for(n=0, 28, if(is(2*n^n), print1(n, ", ")));
CROSSREFS
KEYWORD
nonn
AUTHOR
Altug Alkan, Jan 14 2016
EXTENSIONS
a(13) from Michael De Vlieger, Jan 15 2016
a(14)-a(60) from Chai Wah Wu, Jan 18 2016
STATUS
approved