login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A225765 Least k>0 such that k^3+n is prime, or 0 if there is no such k. 6
1, 1, 2, 1, 2, 1, 4, 0, 2, 1, 2, 1, 6, 3, 2, 1, 6, 1, 4, 3, 2, 1, 2, 5, 4, 3, 0, 1, 2, 1, 10, 3, 2, 3, 2, 1, 4, 5, 2, 1, 6, 1, 4, 3, 2, 1, 6, 5, 4, 11, 2, 1, 2, 5, 6, 3, 8, 1, 2, 1, 6, 3, 2, 0, 2, 1, 4, 5, 10, 1, 2, 1, 4, 3, 2, 3, 6, 1, 24, 3, 2, 1, 12, 13, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

See A225768 for motivation.

a(n) = 0 for n = m^3 (m > 1) but are there other cases of a(n)=0? - Zak Seidov, Nov 10 2014

LINKS

Table of n, a(n) for n=1..85.

EXAMPLE

a(7)=4 because 1^3+7=8, 2^3+7=15, 3^3+7=34 are all composite, but 4^3+7=71 is prime.

a(8)=0 because x^3+8 = (x+2)(x^2-2x+4) is composite for all integer values x>0.

PROG

(PARI) A225765(a, b=3)={#factor(x^b+a)~==1&for(n=1, 9e9, ispseudoprime(n^b+a)&return(n)); a==1&return(1); print1("/*"factor(x^b+a)"*/")}  \\  For illustrative purpose only: the polynomial is factored to avoid an infinite search loop when it is composite. But this does not exclude that all but one factors might equal 1, therefore the factorization is printed for control before 0 is returned.

(PARI) a(n) = {if ((n!=1) && ispower(n, 3), return (0)); k = 1; while (! isprime(k^3+n), k++); k; } \\ Michel Marcus, Nov 10 2014

CROSSREFS

See A085099, A225766, A225767, A225768 for the k^2, k^4, k^5, k^6 analog.

Sequence in context: A137752 A328318 A081169 * A300588 A030359 A324575

Adjacent sequences:  A225762 A225763 A225764 * A225766 A225767 A225768

KEYWORD

nonn

AUTHOR

M. F. Hasler, Jul 25 2013

EXTENSIONS

More terms from Michel Marcus, Nov 10 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 23 22:16 EST 2020. Contains 331177 sequences. (Running on oeis4.)