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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

Table of n, a(n) for n=1..12.

H. Lifchitz and R. Lifchitz, PRP Top Records. Search for x^y+y^x

Derek Orr, Table for n, a(n) for n = 1..100 (unknown k-values are marked "unknown")

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.)