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

1,1

Comments

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

Links

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

Example

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

Prog

(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

Crossrefs

Cf. A180241, A180242, A256613, A255830.

Sequence in context: A076190 A028885 A228233 * A229064 A024910 A283771

Adjacent sequences: A256088 A256089 A256090 * A256092 A256093 A256094

Keyword

nonn

Author

M. F. Hasler, Apr 04 2015

Extensions

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

Status

approved