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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
2, 4, 5, 9, 279, 15331, 1685775, 205670529 (list; graph; refs; listen; history; text; internal format)
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, n-1, if(isprime(k^i-(k%2)-1), c++)); if(c==n-1&&!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

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Last modified May 26 03:20 EDT 2017. Contains 287073 sequences.