

A245511


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


6



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
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OFFSET

2,3


COMMENTS

The locution "largest odd number < n^m" means n^m1 for even n and n^m2 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 2^11 is 1, which is not a prime.
a(5)=3 because the numbers 5^k2, 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=3d; k=1; while(1, if(!isprime(n^kd), v[n1]=k; break, k++)); ); return(v); }
a=avector(10000) \\ For nmax=6000000 runs out of 1GB memory


CROSSREFS

Cf. A245509, A245510, A245512, A245513, A245514.
Sequence in context: A103509 A252941 A069898 * A259940 A228829 A341982
Adjacent sequences: A245508 A245509 A245510 * A245512 A245513 A245514


KEYWORD

nonn


AUTHOR

Stanislav Sykora, Jul 24 2014


STATUS

approved



