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A230769
Numbers k such that (k+1)*2^k - 1 is prime.
4
1, 2, 3, 4, 5, 9, 14, 15, 16, 27, 45, 122, 125, 213, 242, 256, 263, 290, 855, 1059, 2273, 3945, 3999, 9512, 14127, 16486, 20056, 28834, 41493, 159147, 227139, 587823
OFFSET
1,2
COMMENTS
1, 2 and 5 are the only terms of this sequence which are also in A029544. - Gerasimov Sergey, Feb 23 2014
The next term with this property is > 10000. - Michael B. Porter, Feb 23 2014
The probability of a given number N being a twin prime grows like 1/(log(N))^2, so for a given n, the probability that it has this property is 1/n^2, and the sum converges. Are there any n for which n*2^n-1 and n*2^n+1 are both prime? - Michael B. Porter, Feb 25 2014
We can write (k+1)*2^k - 1 = {(k+1)/2}*4^{(k+1)/2} - 1, and when k is odd, this takes the form of a generalized Woodall prime (base 4). These are listed in A086661. In other words, {2*A086661 - 1} gives all the odd terms of this sequence. - Jeppe Stig Nielsen, Oct 16 2019
The largest odd term currently known is 3986381 = 2*A086661(21) - 1. - Jeppe Stig Nielsen, Oct 16 2019
PROG
(PARI) is_A230769(n) = ispseudoprime((n+1)*2^n-1) \\ M. F. Hasler, Mar 01 2014
CROSSREFS
KEYWORD
nonn,more,hard
AUTHOR
Zak Seidov, Feb 23 2014
EXTENSIONS
Edited and extended to values > 2273 by M. F. Hasler, Mar 01 2014
More terms from Jeppe Stig Nielsen, Oct 16 2019
STATUS
approved