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A108714 a(n)=minimal value of k, such that n^2+k^2 or (n^2+k^2)/2 are primes. 11
1, 1, 1, 1, 1, 1, 2, 3, 1, 1, 1, 7, 2, 1, 1, 1, 2, 5, 1, 1, 4, 5, 3, 1, 1, 1, 2, 5, 1, 11, 4, 3, 2, 5, 1, 1, 2, 3, 1, 1, 4, 5, 3, 9, 1, 5, 2, 13, 1, 7, 1, 3, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

COMMENTS

I am attempting to complete a proof that for every natural number n, there is at least one prime of the form n^2+k^2 or (n^2+k^2)/2 with 1<=k<=n.

LINKS

Table of n, a(n) for n=1..53.

EXAMPLE

a(3)=1 because (3^2+1)/2=5 (prime)

a(7)=2 ------> 7^2+2^2=53 (prime)

a(12)=7 -----> 12^2+7^2=193 (prime)

a(23)=3 -----> (23^2+3^2)/2=269 (prime)

a(48)=13 ----> 48^2+13^2=2473 (prime)

CROSSREFS

Sequence in context: A305807 A205104 A215561 * A135508 A030413 A139434

Adjacent sequences: A108711 A108712 A108713 * A108715 A108716 A108717

KEYWORD

nonn

AUTHOR

Robin Garcia, Jun 20 2005

STATUS

approved

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Last modified January 28 09:26 EST 2023. Contains 359851 sequences. (Running on oeis4.)