

A100348


Numbers n such that n4^k is a prime for all k > 0 with 4^k < n.


2



6, 7, 9, 11, 15, 21, 23, 27, 33, 35, 45, 47, 57, 63, 75, 77, 83, 87, 105, 117, 143, 153, 167, 195, 215, 227, 243, 245, 255, 287, 297, 413, 437, 447, 483, 495, 507, 525, 573, 635, 657, 677, 755, 825, 1113, 1133, 1295, 1487, 1515, 1547, 1617, 1623, 2015, 2043, 2397
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OFFSET

1,1


COMMENTS

The largest term appears to be 5833497. No others < 10^9; conjectured to be finite. Similar to A067528, which also contains 5 and 17, but a more direct generalization of A039669, a problem due to Erdos.


LINKS

Michel Marcus, Table of n, a(n) for n = 1..100
Walter E. Mientka and Roger C. Weitzenkamp, On fplentiful numbers, Journal of Combinatorial Theory, Volume 7, Issue 4, December 1969, Pages 374377


EXAMPLE

27 is here because 274 and 2716 are primes.


MATHEMATICA

lst={}; Do[k=1; While[p=n4^k; p>0 && PrimeQ[p], k++ ]; If[p<=0, AppendTo[lst, n]], {n, 5, 10^7}]; lst


CROSSREFS

Cf. A039669 (n such that n2^k is prime), A067528 (n such that n4^k is prime or 1).
Sequence in context: A258153 A175221 A094010 * A240882 A241266 A095908
Adjacent sequences: A100345 A100346 A100347 * A100349 A100350 A100351


KEYWORD

nonn


AUTHOR

T. D. Noe, Nov 18 2004


STATUS

approved



