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 A272032 Positive integers n such that (q^n + r^n)/(q+r) is prime, where q is the number of consecutive composite numbers smaller than n and r is the number of consecutive composite numbers greater than n. 0
 7, 13, 43, 127, 281 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS All terms are prime (conjecture). The variables q and r are the number of composite numbers between the previous and following successive primes of the number n. They seem to be extremely rare. I checked them for {q,r}<=15 and n < 10^5. Numbers n with q + r = 0 lead to 0/0 and are excluded. - Wolfdieter Lang, Apr 22 2016 LINKS EXAMPLE For a(1)=7, q=1 and r=3, (1^7+3^7)/(1+3)=547, 547 is prime. MATHEMATICA Select[Range[3, 10^3], Function[n, With[{q = n - NextPrime[n, -1] - 1, r = NextPrime@ n - n - 1}, If[q + r == 0, False, PrimeQ[(q^n + r^n)/(q + r)]]]]] (* Michael De Vlieger, Apr 18 2016 *) PROG (PARI) is(n)=my(q=n-precprime(n-1)-1, r=nextprime(n+1)-n-1, t); q+r && denominator(t=(q^n + r^n)/(q+r))==1 && isprime(t) \\ Charles R Greathouse IV, Apr 18 2016 (PARI) list(lim)=my(v=List(), p=2, q=3, t); forprime(r=5, nextprime(lim+1), t=((q-p-1)^q+(r-q-1)^q)/(r-p-2); if(denominator(t)==1 && ispseudoprime(t), listput(v, q)); p=q; q=r); Vec(v) \\ Charles R Greathouse IV, Apr 18 2016 CROSSREFS Cf. A046933. Sequence in context: A047977 A139403 A087820 * A023286 A287685 A159305 Adjacent sequences:  A272029 A272030 A272031 * A272033 A272034 A272035 KEYWORD nonn,more AUTHOR Marc Morgenegg, Apr 18 2016 EXTENSIONS a(1) added by Charles R Greathouse IV, Apr 18 2016 STATUS approved

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Last modified October 18 08:08 EDT 2019. Contains 328146 sequences. (Running on oeis4.)