A245514 Smallest m such that at least one of the two odd numbers which bracket n^m is not a prime.

1, 1, 2, 2, 2, 1, 1, 3, 1, 1, 2, 1, 1, 3, 1, 1, 2, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 2

Author

Stanislav Sykora, Jul 24 2014

Keywords

• nonn

Comments

The locution "the two odd numbers which bracket n^m" indicates the pair (n^m-1,n^m+1) for even n and (n^m-2,n^m+2) for odd n.

The initial records in this sequence are a(2)=1, a(4)=2, a(9)=3, a(102795)=4. No higher value was found up to 5500000. It is not clear whether a(n) is bounded.

Examples

			a(2)=1 because one of the two odd numbers (1,3) which bracket 2^1 is not a prime. a(5)=2 because 5^1 is bracketed by the odd numbers (3,7) which are both prime, while 5^2 is bracketed by the odd numbers (23,27), one of which is not a prime.
The number c=102795 is the smallest one whose powers c^1, c^2, c^3 are all odd-bracketed by primes, while c^4 is not.
		

Links

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

Crossrefs

Cf. A245509, A245510, A245511, A245512, A245513.

Programs

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))||(!isprime(n^k+d)), v[n-1]=k; break, k++)); ); return(v); }
a=avector(10000)  \\ For nmax=6000000 runs out of 1GB memory