A245511 - OEIS

%I #21 Feb 03 2018 12:25:15

%S 1,1,2,3,2,3,2,4,1,1,2,3,2,4,1,1,2,4,2,3,1,1,2,2,1,1,1,1,2,2,2,3,1,1,

%T 1,1,2,2,1,1,2,3,2,2,1,1,2,3,1,1,1,1,2,3,1,1,1,1,2,3,2,3,1,1,1,1,2,3,

%U 1,1,2,2,2,3,1,1,1,1,2,2,1,1,2,2,1,1,1,1,2,2,1,1,1,1,1

%N Smallest m such that the largest odd number < n^m is not prime.

%C The locution "largest odd number < n^m" means n^m-1 for even n and n^m-2 for odd n.

%C 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.

%H Stanislav Sykora, <a href="/A245511/b245511.txt">Table of n, a(n) for n = 2..10000</a>

%e a(2)=1 because 2^1-1 is 1, which is not a prime.

%e 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.

%t 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 *)

%o (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);}

%o a=avector(10000)  \\ For nmax=6000000 runs out of 1GB memory

%Y Cf. A245509, A245510, A245512, A245513, A245514.

%K nonn

%O 2,3

%A _Stanislav Sykora_, Jul 24 2014