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

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, 34, 35, 36, 38, 39, 40, 42, 43, 44, 45, 46, 47, 48, 49, 51, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 83, 84, 86, 87, 88

Offset

1,2

Links

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

Formula

a(n) = n + O(n^(3/4)). - Charles R Greathouse IV, Sep 01 2015

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A107907 A080804 A164386 * A184010 A256827 A175139

Adjacent sequences: A111906 A111907 A111908 * A111910 A111911 A111912

Keyword

nonn

Author

Stefan Steinerberger, Nov 25 2005

Status

approved