OFFSET

1,1

COMMENTS

It appears that primes of this form are much less common than primes of the form m^k-k (A099228).

As N increases, squares <= N outnumber all higher powers <= N by an increasingly wide margin, so the above observation is increasingly a consequence of the fact that primes of the form m^2 + 2 are less common than primes of the form m^2 - 2. Among numbers of these two forms, multiples of 3 make up 2/3 of the former, but none of the latter. - Jon E. Schoenfield, Jun 05 2021

LINKS

Vincenzo Librandi and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from Librandi)

MATHEMATICA

nLim=200000; lst={}; Do[k=2; While[n=m^k+k; n<=nLim, AppendTo[lst, n]; k++ ], {m, 2, Sqrt[nLim]}]; Select[Union[lst], PrimeQ]

PROG

(PARI) list(lim)=my(v=List()); for(e=2, logint(lim\=1, 2), forstep(n=3-e%2, sqrtnint(lim-e, e), 2, my(t=n^e+e); if(isprime(t), listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Jun 23 2023

CROSSREFS

KEYWORD

nonn

AUTHOR

T. D. Noe, Oct 06 2004

STATUS

approved