cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A152044 #15 Jan 17 2025 09:10:42
%S A152044 0,1,15,16,65,80,81,175,240,255,256,369,544,609,624,625,671,1040,1105,
%T A152044 1215,1280,1295,1296,1695,1776,2145,2320,2385,2400,2401,2465,2800,
%U A152044 3439,3471,3840,4015,4080,4095,4096,4160,4641,5265,5904,5936,6095,6305,6480
%N A152044 Numbers expressible as the difference of two nonnegative fourth powers.
%C A152044 This sequence seems to grow quadratically. Does a(n) ~ k*n^2 for some k? - _Charles R Greathouse IV_, Jan 16 2025
%H A152044 Charles R Greathouse IV, <a href="/A152044/b152044.txt">Table of n, a(n) for n = 1..10000</a>
%e A152044 E.g. 15=2^4-1^4, 175=4^4-3^4
%t A152044 Select[Abs[Differences/@Tuples[Range[0,12]^4,2]]//Flatten//Union,#<= 6500&] (* _Harvey P. Dale_, Sep 14 2020 *)
%o A152044 (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
%o A152044 (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
%Y A152044 Contains A000583 and A147857 as subsequences. - Chandler
%Y A152044 Cf. A042965, A152043, A152045.
%K A152044 nonn
%O A152044 1,3
%A A152044 Mark Taggart (mt2612f(AT)aol.com), Nov 21 2008
%E A152044 Extended by _Ray Chandler_, Dec 04 2008
%E A152044 Definition corrected by _Harvey P. Dale_, Jan 19 2018