

A067528


Numbers n such that n  4^k is a prime or 1 for all k > 0 and n > 4^k.


5



5, 6, 7, 9, 11, 15, 17, 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
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OFFSET

1,1


COMMENTS

Is the sequence finite?
The last term appears to be 5833497.  T. D. Noe, Nov 23 2004
A less strict version of A039669, n  2^k is prime for 0 < k < log_2 k. If a number is in that sequence, then obviously it is also in this sequence. As of this writing, 105 is believed to be the last term of that sequence.  Alonso del Arte, May 24 2017


LINKS

T. D. Noe, Table of n, a(n) for n=1..102 (no others < 2*10^9)


EXAMPLE

167 is a term as 167  4 = 163, 167  16 = 151, 167  64 = 103 are primes.


MAPLE

filter:= proc(n) local k, t;
for k from 1 do
if 4^k >= n1 then return true
elif not isprime(n4^k) then return false
fi
od
end proc:
select(filter, [$5..3000]); # Robert Israel, May 24 2017


MATHEMATICA

A067528 = {}; Do[k = 1; While[p = n  4^k; p > 0 && (p == 1  PrimeQ[p]), k++]; If[p <= 0, AppendTo[A067528, n]], {n, 5, 10^7}]; A067528 (* T. D. Noe *)


CROSSREFS

Cf. A067526.
Sequence in context: A355239 A030388 A031059 * A287087 A180939 A229231
Adjacent sequences: A067525 A067526 A067527 * A067529 A067530 A067531


KEYWORD

nonn


AUTHOR

Amarnath Murthy, Feb 17 2002


EXTENSIONS

More terms from Sascha Kurz, Mar 19 2002


STATUS

approved



