A256091 Numbers D such that D^2 = A^3 + B^4 + C^5 for some positive integers A, B, C.

5, 7, 9, 11, 17, 23, 25, 33, 38, 45, 55, 72, 79, 89, 95, 96, 99, 100, 103, 105, 117, 133, 137, 163, 171, 213, 218, 220, 237, 239, 240, 248, 255, 257, 282, 303, 305, 320, 347, 355, 362, 375, 384, 393, 407, 408, 411, 459, 475, 503, 506, 513, 525, 539, 540, 567, 581, 613, 616, 657, 659, 660, 751, 752, 761, 792, 796, 808, 824, 833

Offset: 1

Author

M. F. Hasler, Apr 04 2015

Keywords

• nonn

Comments

(8^n*(4^n+8); n = 0, 1, 2, ...) is an infinite subsequence of the subsequence A256613: see that entry for more details.

Examples

			(A, B, C) = (1, 4, 2): 1^3 + 4^4 + 2^5 = 1 + 256 + 32 = 289 = 17^2, so 17 is a term.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A180241, A180242, A256613, A255830.

Programs

PARI

for(D=3,9999,for(C=1,sqrtn(D^2-2,5),for(B=1,sqrtn(D^2-C^5-1,4),ispower(D^2-C^5-B^4,3)&&print1(D","))))

PARI

for(D=3, 9999, ok = 0; for(C=1, sqrtn(D^2-2, 5), for(B=1, sqrtn(D^2-C^5-1, 4), ispower(D^2-C^5-B^4, 3)&&(ok=1)&&print1(D", "); if (ok, break)); if (ok, break))) \\ Michel Marcus, Apr 26 2015

Extensions

Inserted a(5)=17 and removed the doublet 525 by Lars Blomberg, Apr 26 2015