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A275749
Prime numbers of the form 2*4^n - 27.
4
5, 101, 524261, 8388581
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.
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
KEYWORD
nonn,more
AUTHOR
Timothy L. Tiffin, Aug 07 2016
STATUS
approved