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 A275749 Prime numbers of the form 2*4^n - 27. 4
 5, 101, 524261, 8388581 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. 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, a(6) = 2*4^1263 - 27 > 5.0442 * 10^760 a(7) = 2*4^2661 - 27 > 2.4136 * 10^1602 a(8) = 2*4^3165 - 27 > 6.6206 * 10^1905 a(9) > 2*4^5000 - 27 > 3.9901 * 10^3010. 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. LINKS Timothy L. Tiffin, Table of n, a(n) for n = 1..5 D. Alpern, Factorization using the Elliptic Curve Method. FORMULA a(m) = 2*4^A275767(m) - 27. EXAMPLE a(1) = 2*4^A275767(1) - 27 = 2*4^2 - 27 = 32 - 27 = 5. a(2) = 2*4^A275767(2) - 27 = 2*4^3 - 27 = 128 - 27 = 101. a(3) = 2*4^A275767(3) - 27 = 2*4^9 - 27 = 524288 - 27 = 524261. a(4) = 2*4^A275767(4) - 27 = 2*4^11 - 27 = 8388608 - 27 = 8388581. MATHEMATICA Select[2*4^Range[2, 200] - 27, PrimeQ] (* Michael De Vlieger, Aug 08 2016 *) CROSSREFS Cf. A275701, A275750, A275767. Sequence in context: A349045 A337831 A337828 * A057207 A124986 A231830 Adjacent sequences: A275746 A275747 A275748 * A275750 A275751 A275752 KEYWORD nonn,more AUTHOR Timothy L. Tiffin, Aug 07 2016 STATUS approved

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Last modified May 29 18:36 EDT 2024. Contains 372952 sequences. (Running on oeis4.)