The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A214891 Numbers that are not the sum of two squares and two fourth powers. 2
 23, 44, 71, 79, 184, 368, 519, 599, 704, 1136, 1264, 2944, 4024, 5888, 8304, 9584, 11264, 18176, 20224, 47104, 64384, 94208, 132864, 153344, 180224, 290816, 323584, 753664, 1030144, 1507328, 2125824, 2453504, 2883584, 4653056, 5177344, 12058624, 16482304 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS From XU Pingya, Feb 07 2018: (Start) When n is a term, 16n is also. This can been proved as follows: (1) If w is odd, then 16n - w^4 == 7 (mod 8), and it follows from Legendre's three-square theorem that the equation x^2 + y^2 + z^4 + w^4 = 16n has no solution (it is the same when x, y or z are odd numbers). (2) If x, y, z and w are even numbers (x = 2a, y = 2b, z = 2c, w = 2d) such that x^2 + y^2 + z^4 + w^4 = 16n, then a^2 + b^2 = 4(n - c^4 - d^4). So there are integers u and v satisfying u^2 + v^2 = n - c^4 - d^4. i.e. u^2 + v^2 + c^4 + d^4 = n, which is a contradiction. (End) LINKS Donovan Johnson, Table of n, a(n) for n = 1..52 (terms <= 4*10^9) PROG (PARI) N=10^6;  x='x+O('x^N); S(e)=sum(j=0, ceil(N^(1/e)), x^(j^e)); v=Vec( S(4)^2 * S(2)^2 ); for(n=1, #v, if(!v[n], print1(n-1, ", "))); CROSSREFS Cf. A001481, A004999, A022549. Sequence in context: A138975 A168439 A198949 * A003859 A058545 A161709 Adjacent sequences:  A214888 A214889 A214890 * A214892 A214893 A214894 KEYWORD nonn AUTHOR Joerg Arndt, Jul 29 2012 EXTENSIONS a(29)-a(37) from Donovan Johnson, Jul 29 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 22 16:29 EST 2020. Contains 331152 sequences. (Running on oeis4.)