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A122540 Primes that can be written in n ways as the sum of three fourth powers. 3
2, 137633, 409698593 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If you replace 'prime' with 'odd number', the sequence is 17, 2673, 16196193, 155129315313, ... Next term is at least 3000^4.

The restriction to primes is quite severe and to odd numbers reasonably so; otherwise x^4+y^4+(x+y)^4=2(x^2+xy+y^2)^2 gives very many examples of the form 2k^2.

LINKS

Table of n, a(n) for n=1..3.

EXAMPLE

a(2)=137633; 8^4+13^4+18^4 = 9^4+16^4+16^4 and this is the smallest prime N for which this holds

a(3)=409698593; 128^4+109^4+18^4 = 129^4+94^4+86^4 = 142^4+42^4+1

CROSSREFS

Obvious variant on A085559.

Sequence in context: A170995 A319022 A003840 * A324438 A167518 A178168

Adjacent sequences:  A122537 A122538 A122539 * A122541 A122542 A122543

KEYWORD

hard,more,nonn,bref

AUTHOR

Thomas Womack (tom(AT)womack.net), Sep 19 2006

STATUS

approved

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Last modified October 20 19:49 EDT 2021. Contains 348118 sequences. (Running on oeis4.)