A245511 Smallest m such that the largest odd number < n^m is not prime.

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, 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, 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

Offset: 2

Author

Stanislav Sykora, Jul 24 2014

Keywords

• nonn

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.

Examples

			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.
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 2..10000

Crossrefs

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

Programs

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 *)

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