OFFSET
2,3
COMMENTS
The locution "largest odd number < n^m" means n^m-1 for even n and n^m-2 for odd n.
The record values in this sequence are a(2)=1, a(4)=2, a(5)=3, a(9)=4, a(279)=5, a(15331)=6, a(1685775)=7. No higher value was found up to 5500000 (see also A245512). It is not clear whether a(n) is bounded.
LINKS
Stanislav Sykora, Table of n, a(n) for n = 2..10000
EXAMPLE
a(2)=1 because 2^1-1 is 1, which is not a prime.
a(5)=3 because the numbers 5^k-2, for k=1,2,3,.., are 3,23,123,... and the first nonprime among them corresponds to k=3.
MATHEMATICA
f[n_] := Block[{m = 1, d = If[ OddQ@ n, 2, 1]}, While[t = n^m - d; EvenQ@ t || PrimeQ@ t, m++]; m]; Array[f, 105, 2] (* Robert G. Wilson v, Aug 04 2014 *)
PROG
(PARI) avector(nmax)={my(n, k, d=2, v=vector(nmax)); for(n=2, #v+1, d=3-d; k=1; while(1, if(!isprime(n^k-d), v[n-1]=k; break, k++)); ); return(v); }
a=avector(10000) \\ For nmax=6000000 runs out of 1GB memory
CROSSREFS
KEYWORD
nonn
AUTHOR
Stanislav Sykora, Jul 24 2014
STATUS
approved