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

1,3

Links

Jinyuan Wang, Table of n, a(n) for n = 1..1500 (terms 1..500 from Nathaniel Johnston)

Example

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.

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

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 *)

Prog

(PARI) a(n) = my(x=(2^n-1)*2^n); x - precprime(x); \\ Michel Marcus, Feb 21 2019

Crossrefs

Cf. A098845, A191001, A191620.

Cf. A020522 ((2^n-1)*2^n).

Sequence in context: A134836 A180955 A349182 * A285409 A208510 A131767

Adjacent sequences: A191748 A191749 A191750 * A191752 A191753 A191754

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jun 14 2011, Jun 15 2011

Status

approved