A152044 Numbers expressible as the difference of two nonnegative fourth powers.

0, 1, 15, 16, 65, 80, 81, 175, 240, 255, 256, 369, 544, 609, 624, 625, 671, 1040, 1105, 1215, 1280, 1295, 1296, 1695, 1776, 2145, 2320, 2385, 2400, 2401, 2465, 2800, 3439, 3471, 3840, 4015, 4080, 4095, 4096, 4160, 4641, 5265, 5904, 5936, 6095, 6305, 6480

Offset

1,3

Comments

Contains A000583 and A147857 as subsequences. - Chandler

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

E.g. 15=2^4-1^4, 175=4^4-3^4

Mathematica

Select[Abs[Differences/@Tuples[Range[0, 12]^4, 2]]//Flatten//Union, #<= 6500&] (* Harvey P. Dale, Sep 14 2020 *)

Prog

(PARI) is(n)=if(n<1, return(!n)); for(m=sqrtnint(n-1, 4)+1, sqrtnint(n\4, 3)+1, if(ispower(m^4-n, 4), return(1))); 0 \\ Charles R Greathouse IV, Sep 04 2013
(PARI) lst(lim)=my(v=List([0]), t); lim\=1; for(n=1, sqrtnint(lim\4, 3)+1, for(m=sqrtnint(max(n^4-lim, 0), 4), n-1, t=n^4-m^4; if(t<=lim, listput(v, t)))); vecsort(Vec(v), , 8) \\ Charles R Greathouse IV, Sep 04 2013

Crossrefs

Cf. A042965, A152043, A152045.

Sequence in context: A041460 A041466 A332008 * A041468 A041470 A041472

Adjacent sequences: A152041 A152042 A152043 * A152045 A152046 A152047

Keyword

nonn

Author

Mark Taggart (mt2612f(AT)aol.com), Nov 21 2008

Extensions

Extended by Ray Chandler, Dec 04 2008

Definition corrected by Harvey P. Dale, Jan 19 2018

Status

approved