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A245510 Records in A245509: smallest m > 1 such that the first odd number greater than m^k is prime for every 0 < k < n, but not for k = n. 5
7, 5, 2, 105, 3, 909, 4995825, 28212939 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For more comments and a program, see A245509. a(9), if it exists, certainly exceeds 1050000000. 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(4) = 105 because 105 is the smallest m such that the first odd numbers after m^k are prime for k = 1,2,3, but composite for k = 4.

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 < 29000000, 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, A245511, A245512, A245513, A245514.

Sequence in context: A021934 A021097 A087273 * A199794 A106040 A085927

Adjacent sequences:  A245507 A245508 A245509 * A245511 A245512 A245513

KEYWORD

nonn,hard,more

AUTHOR

Stanislav Sykora, Jul 24 2014

EXTENSIONS

a(4) and example 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 22 16:19 EDT 2017. Contains 286882 sequences.