

A245512


Records in A245511: smallest m > 1 such that the largest odd number less than m^k is prime for every 0 < k < n, but not for k = n.


5




OFFSET

1,1


COMMENTS

For more comments and a program, see A245511. a(9), if it exists, certainly exceeds 500000000. It is not clear whether this sequence is infinite, nor whether a(n) is defined for every n.


LINKS

Table of n, a(n) for n=1..8.


EXAMPLE

a(3) = 5 because the odd numbers preceding 5^k, for k = 1,2,3, are 3, 23 and 123, and the first one which is not a prime corresponds to k = 3. Moreover, 5 is the smallest natural having this property.


MATHEMATICA

f[n_] := Block[{d = If[ OddQ@ n, 2, 1], m = 1, t}, While[t = n^m  d; EvenQ@ t  PrimeQ@ t, m++]; m]; t = Table[0, {25}]; k = 2; While[k < 210000000, a = f@ k; If[ t[[a]] == 0, t[[a]] = k; Print[{a, k}]]; k++]; t (* Robert G. Wilson v, Aug 04 2014 *)


PROG

(PARI)
a(n) = for(k=1, 10^6, c=0; for(i=1, n1, if(isprime(k^i(k%2)1), c++)); if(c==n1&&!isprime(k^n(k%2)1), return(k)))
n=1; while(n<10, print1(a(n), ", "); n++) \\ Derek Orr, Jul 27 2014


CROSSREFS

Cf. A245509, A245510, A245511, A245513, A245514.
Sequence in context: A067298 A077389 A122991 * A232616 A125728 A276608
Adjacent sequences: A245509 A245510 A245511 * A245513 A245514 A245515


KEYWORD

nonn,hard,more


AUTHOR

Stanislav Sykora, Jul 24 2014


EXTENSIONS

a(4) corrected by Derek Orr, Jul 27 2014
a(8) from Robert G. Wilson v, Aug 04 2014


STATUS

approved



