This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A275749 #47 Feb 27 2025 15:07:22 %S A275749 5,101,524261,8388581 %N A275749 Prime numbers of the form 2*4^k - 27. %C A275749 Values of the exponent k 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 A275749 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 A275749 a(6) = 2*4^1263 - 27 > 5.0442 * 10^760 %C A275749 a(7) = 2*4^2661 - 27 > 2.4136 * 10^1602 %C A275749 a(8) = 2*4^3165 - 27 > 6.6206 * 10^1905 %C A275749 a(9) > 2*4^5000 - 27 > 3.9901 * 10^3010. %C A275749 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 A275749 Timothy L. Tiffin, <a href="/A275749/b275749.txt">Table of n, a(n) for n = 1..5</a> %H A275749 D. Alpern, <a href="https://www.alpertron.com.ar/ECM.HTM">Factorization using the Elliptic Curve Method</a>. %F A275749 a(n) = 2*4^A275767(n) - 27. %e A275749 a(1) = 2*4^A275767(1) - 27 = 2*4^2 - 27 = 32 - 27 = 5. %e A275749 a(2) = 2*4^A275767(2) - 27 = 2*4^3 - 27 = 128 - 27 = 101. %e A275749 a(3) = 2*4^A275767(3) - 27 = 2*4^9 - 27 = 524288 - 27 = 524261. %e A275749 a(4) = 2*4^A275767(4) - 27 = 2*4^11 - 27 = 8388608 - 27 = 8388581. %t A275749 Select[2*4^Range[2, 200] - 27, PrimeQ] (* _Michael De Vlieger_, Aug 08 2016 *) %Y A275749 Cf. A275701, A275750, A275767. %K A275749 nonn %O A275749 1,1 %A A275749 _Timothy L. Tiffin_, Aug 07 2016