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%I #9 May 12 2013 04:56:33
%S 6,7,9,11,15,21,23,27,33,35,45,47,57,63,75,77,83,87,105,117,143,153,
%T 167,195,215,227,243,245,255,287,297,413,437,447,483,495,507,525,573,
%U 635,657,677,755,825,1113,1133,1295,1487,1515,1547,1617,1623,2015,2043,2397
%N Numbers n such that n-4^k is a prime for all k > 0 with 4^k < n.
%C 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.
%H Michel Marcus, <a href="/A100348/b100348.txt">Table of n, a(n) for n = 1..100</a>
%H Walter E. Mientka and Roger C. Weitzenkamp, <a href="http://dx.doi.org/10.1016/S0021-9800(69)80067-0">On f-plentiful numbers</a>, Journal of Combinatorial Theory, Volume 7, Issue 4, December 1969, Pages 374-377
%e 27 is here because 27-4 and 27-16 are primes.
%t lst={}; Do[k=1; While[p=n-4^k; p>0 && PrimeQ[p], k++ ]; If[p<=0, AppendTo[lst, n]], {n, 5, 10^7}]; lst
%Y Cf. A039669 (n such that n-2^k is prime), A067528 (n such that n-4^k is prime or 1).
%K nonn
%O 1,1
%A _T. D. Noe_, Nov 18 2004