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A191751 Least k such that (2^n-1)*2^n - k is a prime number. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 1..500

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, A191620.

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

Sequence in context: A114278 A134836 A180955 * 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

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Last modified October 16 07:30 EDT 2019. Contains 328051 sequences. (Running on oeis4.)