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%I #43 Aug 11 2016 02:48:39
%S 5,101,524261,8388581
%N Prime numbers of the form 2*4^n - 27.
%C Values of the exponent n are given in A275767, and every exponent (except for the first one) is odd. Consequently, after a(1) = 5, the rightmost digit of each term in this sequence will be 1.
%C As seen in the link below, a(5) = 2*4^291 - 27 > 3.1658 * 10^175. As a result of the recent extensions to A275767 by _Vincenzo Librandi_,
%C a(6) = 2*4^1263 - 27 > 5.0442 * 10^760
%C a(7) = 2*4^2661 - 27 > 2.4136 * 10^1602
%C a(8) = 2*4^3165 - 27 > 6.6206 * 10^1905
%C a(9) > 2*4^5000 - 27 > 3.9901 * 10^3010.
%C These primes a(m) can be used to generate numbers having abundance 26. The formula a(m)*(a(m)+27)/2 produces some of the terms in A275701.
%H Timothy L. Tiffin, <a href="/A275749/b275749.txt">Table of n, a(n) for n = 1..5</a>
%H D. Alpern, <a href="https://www.alpertron.com.ar/ECM.HTM">Factorization using the Elliptic Curve Method</a>.
%F a(m) = 2*4^A275767(m) - 27.
%e a(1) = 2*4^A275767(1) - 27 = 2*4^2 - 27 = 32 - 27 = 5.
%e a(2) = 2*4^A275767(2) - 27 = 2*4^3 - 27 = 128 - 27 = 101.
%e a(3) = 2*4^A275767(3) - 27 = 2*4^9 - 27 = 524288 - 27 = 524261.
%e a(4) = 2*4^A275767(4) - 27 = 2*4^11 - 27 = 8388608 - 27 = 8388581.
%t Select[2*4^Range[2, 200] - 27, PrimeQ] (* _Michael De Vlieger_, Aug 08 2016 *)
%Y Cf. A275701, A275750, A275767.
%K nonn,more
%O 1,1
%A _Timothy L. Tiffin_, Aug 07 2016
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