A286812 a(n) = 105 - 2^n.

104, 103, 101, 97, 89, 73, 41, -23, -151, -407, -919, -1943, -3991, -8087, -16279, -32663, -65431, -130967, -262039, -524183, -1048471, -2097047, -4194199, -8388503, -16777111, -33554327, -67108759, -134217623, -268435351, -536870807, -1073741719, -2147483543

Offset

0,1

Comments

Perhaps m = 105 is the largest number such that m - 2^n is prime for all 1 < n < log_2 m. Indeed 105 - 2^n is also prime for quite a few n > 6.7142455... For n = 9 we have 105 - 512 = -407 = (-1) * 11 * 37, the first instance of a composite term after a(0).

Links

Table of n, a(n) for n=0..31.

Erich Friedman, What's Special About This Number? Entry for 105.

Index entries for linear recurrences with constant coefficients, signature (3,-2).

Formula

G.f.: (104 - 209*x)/((1 - x)*(1 - 2*x)). - Bruno Berselli, May 22 2017

Mathematica

105 - 2^Range[0, 31]

Prog

(PARI) vector(40, n, n--; 105-2^n) \\ Bruno Berselli, May 22 2017
(Python) [105-2**n for n in range(40)] # Bruno Berselli, May 22 2017
(Sage) [105-2^n for n in range(40)] # Bruno Berselli, May 22 2017
(Magma) [105-2^n: n in [0..40]]; // Bruno Berselli, May 22 2017

Crossrefs

Cf. A000079.

Sequence in context: A091025 A054904 A117845 * A328782 A163554 A045208

Adjacent sequences: A286809 A286810 A286811 * A286813 A286814 A286815

Keyword

sign,easy

Author

Alonso del Arte, May 21 2017

Status

approved