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 A243147 Least number k such that n^k + k^n is prime or 0 if no such k exists. 2
 1, 1, 2, 1, 24, 1, 54, 69, 2, 1, 3100, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS More terms given in links. a(n) = 1 if and only if n + 1 is prime. Thus there are infinitely many nonzero entries. For n in A016767, a(n) = 0 since n^k + k^n is factorable and will never be prime. Thus there are infinitely many zero entries. If a(i) = j then a(j) <= i for all i and j not equal to 0. a(n) and n must have opposite parity. If n is odd/even, a(n) must be even/odd, respectively. Further, gcd(n, a(n)) = 1 for all n. LINKS H. Lifchitz and R. Lifchitz, PRP Top Records. Search for x^y+y^x EXAMPLE 3^1 + 1^3 = 4 is not prime. 3^2 + 2^3 = 17 is prime. So a(3) = 2. PROG (PARI) a(n)=if(ispower(n)&&ispower(n)%3==0&&n%3==0, return(0)); k=1; while(!ispseudoprime(n^k+k^n), k++); return(k) vector(12, n, a(n)) CROSSREFS Cf. A016767. Sequence in context: A108778 A271530 A062763 * A261407 A037943 A073876 Adjacent sequences:  A243144 A243145 A243146 * A243148 A243149 A243150 KEYWORD nonn,hard,more AUTHOR Derek Orr, May 30 2014 STATUS approved

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Last modified September 22 03:54 EDT 2020. Contains 337289 sequences. (Running on oeis4.)