A239247 Numbers n such that n^4 can be written as a sum of five distinct positive 4th powers.
15, 30, 35, 45, 55, 60, 65, 70, 75, 85, 89, 90, 95, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 165, 170, 175, 178, 180, 185, 190, 195, 205, 210, 215, 220, 225, 230, 233, 235, 240, 245, 250, 255, 260, 265, 267, 270, 275, 280, 285, 290, 295, 300
Offset: 1
Keywords
Examples
15^4 = 4^4 + 6^4 + 8^4 + 9^4 + 14^4. 35^4 = 4^4 + 21^4 + 22^4 + 26^4 + 28^4. 55^4 = 2^4 + 13^4 + 16^4 + 44^4 + 48^4. 65^4 = 1^4 + 8^4 + 12^4 + 32^4 + 64^4. 85^4 = 2^4 + 13^4 + 32^4 + 34^4 + 84^4. 89^4 = 10^4 + 35^4 + 52^4 + 60^4 + 80^4. 95^4 = 6^4 + 48^4 + 66^4 + 67^4 + 78^4. 115^4 = 4^4 + 31^4 + 48^4 + 58^4 + 112^4. 125^4 = 8^4 + 11^4 + 26^4 + 84^4 + 118^4. 145^4 = 2^4 + 23^4 + 46^4 + 52^4 + 144^4. 155^4 = 6^4 + 39^4 + 88^4 + 96^4 + 144^4. 185^4 = 2^4 + 38^4 + 62^4 + 87^4 + 182^4. 205^4 = 4^4 + 133^4 + 142^4 + 146^4 + 156^4. 215^4 = 4^4 + 26^4 + 127^4 + 174^4 + 176^4. 233^4 = 40^4 + 65^4 + 94^4 + 150^4 + 220^4. 235^4 = 9^4 + 52^4 + 148^4 + 184^4 + 194^4.
Links
- Lars Blomberg, Table of n, a(n) for n = 1..7560 (terms < 10000)
- Lars Blomberg, Primitive solutions for terms < 10000. Only the first solution found for each term is included.
- Eric Weisstein's World of Mathematics, Diophantine Equation 4th Powers.
Programs
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PARI
isok(n) = {ret = 0; for (x=1, sqrtnint(n^4\5, 4), for (y=x+1, sqrtnint((n^4 - x^4)\4, 4), for (z=y+1, sqrtnint((n^4 - x^4 - y^4)\3, 4), for (t=z+1, sqrtnint((n^4 - x^4 - y^4 - z^4)\2, 4), for (u=t+1, sqrtnint((n^4 - x^4 - y^4 - z^4 - t^4), 4), if (x^4+y^4+z^4+t^4+u^4 == n^4, print(n, ": ", x, ", ", y, ", ",z ,", ",t, ", ",u); ret = 1;);););););); return (ret);}
Formula
a(1) = A130022(4).
Extensions
Missing terms 15 and its multiples found by Alois P. Heinz, Mar 14 2014
More examples from Michel Marcus, Mar 18 2014
More terms from Lars Blomberg, Apr 05 2014
Comments