

A218656


Number of ways to write 2n+1 as x+y with 0<x<y and x^4+y^4 prime.


8



1, 2, 3, 2, 3, 3, 1, 5, 4, 4, 4, 5, 4, 7, 6, 5, 3, 10, 4, 9, 8, 4, 9, 6, 7, 11, 7, 5, 11, 9, 9, 9, 11, 4, 14, 14, 9, 8, 9, 7, 11, 8, 12, 12, 10, 9, 11, 17, 10, 12, 16, 7, 13, 14, 8, 15, 9, 11, 23, 16, 9, 17, 23, 8, 15, 15, 11, 21, 18, 12, 19, 14, 15, 19, 21, 17, 16, 23, 13, 21, 20, 17, 29
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OFFSET

1,2


COMMENTS

Conjecture: a(n)>0 for all n=1,2,3,...
If we replace x^4+y^4 in the definition of a(n) by x^2+y^2, then a(n) was conjectured to be always positive by Thomas Ordowski on Nov 03 2012.
We also have similar conjectures with x^4+y^4 replaced by x^8+y^8 or x^{16}+y^{16}.
Alternate definition: Number of primes of the form k^4+(2n+1k)^4, 0 < k <= n.  M. F. Hasler, Nov 05 2012


REFERENCES

Thomas Ordowski, Personal email message, Nov 03 2012.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..20000


EXAMPLE

For n=7 we have a(7)=1, since x^4+(15x)^4 with 0<x<8 is prime only when x=4.


MAPLE

A218656 := n> add(`if`(isprime(i^4+(2*n+1i)^4), 1, 0), i=1..n): # Alois P. Heinz, Jul 09 2016


MATHEMATICA

a[n_]:=a[n]=Sum[If[PrimeQ[x^4+(2n+1x)^4]==True, 1, 0], {x, 1, n}]
Do[Print[n, " ", a[n]], {n, 1, 20000}]


PROG

(PARI) A218586(n)=sum(x=1, n+0*n=2*n+1, isprime(x^4+(nx)^4)) \\  M. F. Hasler, Nov 05 2012


CROSSREFS

Cf. A002645, A218585, A218654.
Sequence in context: A138960 A245553 A115397 * A200323 A075370 A332297
Adjacent sequences: A218653 A218654 A218655 * A218657 A218658 A218659


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Nov 04 2012


STATUS

approved



