A191751 Least k such that (2^n-1)*2^n - k is a prime number.
0, 1, 3, 1, 1, 5, 3, 11, 1, 1, 25, 29, 3, 13, 3, 7, 39, 1, 13, 23, 3, 5, 69, 11, 39, 13, 15, 31, 99, 83, 117, 31, 9, 11, 25, 67, 45, 1, 39, 47, 45, 71, 69, 77, 1, 131, 67, 101, 55, 1, 9, 41, 13, 43, 33, 233, 1, 113, 7, 29, 45, 55, 99, 41, 261, 5, 15, 343, 9
Offset: 1
Keywords
Examples
a(1)=0 because (2^1-1)*2^1 - 0 = 2 is prime, a(2)=1 because (2^2-1)*2^2 - 1 = 11 is prime, a(3)=3 because (2^3-1)*2^3 - 3 = 53 is prime, a(4)=1 because (2^4-1)*2^4 - 1 = 239 is prime, a(5)=1 because (2^5-1)*2^5 - 1 = 991 is prime, a(6)-5 because (2^6-1)*2^6 - 5 = 4027 is prime.
Links
- Jinyuan Wang, Table of n, a(n) for n = 1..1500 (terms 1..500 from Nathaniel Johnston)
Programs
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Maple
a := proc(n) local k: for k from 0 do if(isprime((2^n-1)*2^n-k))then return k: fi: od: end: seq(a(n), n=1..69); # Nathaniel Johnston, Jun 14 2011
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Mathematica
lk[n_]:=Module[{c=2^n,k=0},While[!PrimeQ[c(c-1)-k],k++];k]; Array[lk,70] (* Harvey P. Dale, Jul 02 2018 *) -
PARI
a(n) = my(x=(2^n-1)*2^n); x - precprime(x); \\ Michel Marcus, Feb 21 2019