|
| |
|
|
A100291
|
|
Numbers of the form a^4 + b^3 with a, b > 0.
|
|
10
|
|
|
|
2, 9, 17, 24, 28, 43, 65, 80, 82, 89, 108, 126, 141, 145, 206, 217, 232, 257, 264, 283, 297, 320, 344, 359, 381, 424, 472, 513, 528, 593, 599, 626, 633, 652, 689, 730, 745, 750, 768, 810, 841, 968, 985, 1001, 1016, 1081, 1137, 1256, 1297, 1304, 1323, 1332
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
LINKS
|
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
|
|
|
MATHEMATICA
|
lst={}; Do[p=a^4+b^3; If[p<2000, AppendTo[lst, p]], {a, 64}, {b, 256}]; Union[lst]
With[{nn=20}, Select[Union[#[[1]]^4+#[[2]]^3&/@Tuples[Range[20], 2]], #<= nn^3+1&]] (* Harvey P. Dale, May 27 2020 *)
|
|
|
PROG
|
(PARI) is(n)=for(a=1, sqrtnint(n-1, 4), ispower(n-a^4, 3) && return(a)) \\ Returns a > 0 if n is in the sequence, or 0 otherwise. - M. F. Hasler, Apr 25 2018
|
|
|
CROSSREFS
|
Cf. A100271 (primes of the form a^4 + b^3).
Cf. A055394 (a^2 + b^3: contains this as subsequence), A111925 (a^2 + b^4), A100291 (a^4 + b^3), A100292 (a^5 + b^2), A100293 (a^5 + b^3), A100294 (a^5 + b^4), A303372 (a^2 + b^6), A303373 (a^3 + b^6), A303374 (a^4 + b^6), A303375 (a^5 + b^6).
Roots of 5th powers are listed in A300565 (z^5 = x^3 + y^4); see also A300564 (z^4 = x^2 + y^3) and A242183, A300566 (z^6 = x^4 + y^5), A300567 (z^7 = x^6 + y^5), A302174.
Sequence in context: A200944 A137189 A028503 * A126082 A083707 A240651
Adjacent sequences: A100288 A100289 A100290 * A100292 A100293 A100294
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
T. D. Noe, Nov 18 2004
|
|
|
EXTENSIONS
|
Edited by M. F. Hasler, Apr 25 2018
|
|
|
STATUS
|
approved
|
| |
|
|
