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A067528 Numbers n such that n - 4^k is a prime or 1 for all k > 0 and n > 4^k.

%I A067528 #18 May 25 2017 04:18:40
%S A067528 5,6,7,9,11,15,17,21,23,27,33,35,45,47,57,63,75,77,83,87,105,117,143,
%T A067528 153,167,195,215,227,243,245,255,287,297,413,437,447,483,495,507,525,
%U A067528 573,635,657,677,755,825,1113,1133,1295,1487,1515,1547,1617,1623,2015
%N A067528 Numbers n such that n - 4^k is a prime or 1 for all k > 0 and n > 4^k.
%C A067528 Is the sequence finite?
%C A067528 The last term appears to be 5833497. - _T. D. Noe_, Nov 23 2004
%C A067528 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
%H A067528 T. D. Noe, <a href="/A067528/b067528.txt">Table of n, a(n) for n=1..102</a> (no others < 2*10^9)
%e A067528 167 is a term as 167 - 4 = 163, 167 - 16 = 151, 167 - 64 = 103 are primes.
%p A067528 filter:= proc(n) local k, t;
%p A067528   for k from 1 do
%p A067528     if 4^k >= n-1 then return true
%p A067528     elif not isprime(n-4^k) then return false
%p A067528     fi
%p A067528   od
%p A067528 end proc:
%p A067528 select(filter, [$5..3000]); # _Robert Israel_, May 24 2017
%t A067528 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_ *)
%Y A067528 Cf. A067526.
%K A067528 nonn
%O A067528 1,1
%A A067528 _Amarnath Murthy_, Feb 17 2002
%E A067528 More terms from _Sascha Kurz_, Mar 19 2002