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A111909 Numbers that cannot be represented as a^4 + b^2 with a, b > 0. 3

%I #9 Dec 06 2015 22:57:41

%S 1,3,4,6,7,8,9,11,12,13,14,15,16,18,19,21,22,23,24,27,28,29,30,31,33,

%T 34,35,36,38,39,40,42,43,44,45,46,47,48,49,51,53,54,55,56,57,58,59,60,

%U 61,62,63,64,66,67,68,69,70,71,72,73,74,75,76,77,78,79,81,83,84,86,87,88

%N Numbers that cannot be represented as a^4 + b^2 with a, b > 0.

%H Charles R Greathouse IV, <a href="/A111909/b111909.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = n + O(n^(3/4)). - _Charles R Greathouse IV_, Sep 01 2015

%e 3 cannot be represented as a^4 + b^2 and thus is in this sequence while 10 = 1^4 + 3^2 is not.

%o (PARI) list(lim)=lim\=1; my(v=List(),u=vectorsmall(lim),m2); for(m=1,sqrtint(lim-1), m2=m^2; for(n=1,sqrtnint(lim-m2,4), u[m2+n^4]=1)); for(i=1,#u, if(!u[i], listput(v,i))); Set(v) \\ _Charles R Greathouse IV_, Sep 01 2015

%Y Cf. A111925 (complement), A055394, A022549. A022544 is a subsequence.

%K nonn

%O 1,2

%A _Stefan Steinerberger_, Nov 25 2005

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Last modified March 28 15:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)