The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”). Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

%I

%S 2,4,5,9,279,15331,1685775,205670529

%N 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.

%C 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.

%e 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.

%t 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 *)

%o (PARI)

%o 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)))

%o n=1;while(n<10,print1(a(n),", ");n++) \\ _Derek Orr_, Jul 27 2014

%Y Cf. A245509, A245510, A245511, A245513, A245514.

%K nonn,hard,more

%O 1,1

%A _Stanislav Sykora_, Jul 24 2014

%E a(4) corrected by _Derek Orr_, Jul 27 2014

%E a(8) from _Robert G. Wilson v_, Aug 04 2014

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 6 13:45 EST 2021. Contains 349563 sequences. (Running on oeis4.)