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A282948 Numbers n such that (u^4 + v^4)/2 = x^4 + y^4 = n has a solution in positive integers u,v,x,y. 1
162401, 2598416, 13154481, 41574656, 101500625, 210471696, 389924801, 665194496, 1065512961, 1624010000, 2377713041, 3367547136, 4638334961, 6238796816, 8221550625, 10643111936, 13563893921, 17048207376, 21164260721, 25984160000, 31583908881, 38043408656 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All terms are composite.

If n is in this sequence, then n*k^4 with k > 0 is in this sequence.

Numbers n such that n and 2*n are both in A003336. - Michel Marcus, Feb 25 2017

The first term which is not a multiple of a(1) is a(84) = 8051889328801. - Giovanni Resta, Feb 25 2017

Based on Giovanni Resta's b-file, the squarefree terms are 162401, 8051889328801, 9305528350081, 16778006844241, .... - Altug Alkan, Feb 26 2017

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..513 (terms < 10^16)

EXAMPLE

(19^4 + 21^4)/2 = 7^4 + 20^4 = 162401.

PROG

(PARI) isA003336(n) = for(k=1, sqrtnint(n\2, 4), ispower(n-k^4, 4) && return(1));

is(n) = isA003336(n) && isA003336(2*n);

(PARI) T=thueinit('x^4+1, 1);

has(n)=#thue(T, n)>0 && !issquare(n)

list(lim)=my(v=List(), x4, t); for(x=1, sqrtnint(lim\=1, 4), x4=x^4; for(y=1, min(sqrtnint(lim-x4, 4), x), t=x4+y^4; if(has(2*t), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 26 2017

CROSSREFS

Cf. A003336, A191345.

Sequence in context: A244348 A083633 A043649 * A230925 A204653 A234989

Adjacent sequences:  A282945 A282946 A282947 * A282949 A282950 A282951

KEYWORD

nonn

AUTHOR

Altug Alkan and Thomas Ordowski, Feb 25 2017

EXTENSIONS

a(10)-a(22) from Giovanni Resta, Feb 25 2017

STATUS

approved

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Last modified October 19 22:28 EDT 2018. Contains 316378 sequences. (Running on oeis4.)