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 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 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

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