A062709 a(n) = 2^n + 3.

4, 5, 7, 11, 19, 35, 67, 131, 259, 515, 1027, 2051, 4099, 8195, 16387, 32771, 65539, 131075, 262147, 524291, 1048579, 2097155, 4194307, 8388611, 16777219, 33554435, 67108867, 134217731, 268435459, 536870915, 1073741827, 2147483651, 4294967299, 8589934595, 17179869187

Offset: 0

Author

Henry Bottomley, Jul 13 2001

Keywords

• nonn
• easy

Comments

Written in binary a(n) is 1000...00011 for n > 1.

For n >= 2, a(n) is the minimal k for which A000120(k(2^n-1)) is not multiple of n. - Vladimir Shevelev, Jun 05 2009

Examples

			a(3) = 2^3 + 3 = 8 + 3 = 11.
a(4) = 2^4 + 3 = 16 + 3 = 19.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

Primes in this sequence are A057733.

Cf. A000051, A000079, A000120, A000225, A004119, A030101, A052548, A173921.

Programs

Magma

[2^n+3: n in [0..40]] // Vincenzo Librandi, Jan 31 2012

Mathematica

LinearRecurrence[{3, -2}, {4, 5}, 40] (* Vincenzo Librandi, Jan 31 2012 *)
NestList[2 * # - 3 &, 4, 20] (* Zak Seidov, Mar 28 2015 *)
2^Range[0, 29] + 3 (* Alonso del Arte, Mar 28 2015 *)

PARI

a(n)=2^n+3 \\ Charles R Greathouse IV, Jan 30 2012

Sage

[gaussian_binomial(n,1,2)+4 for n in range(0,32)] # Zerinvary Lajos, May 31 2009

Formula

a(n) = 2a(n-1) - 3 = A052548(n) + 1 = A000051(n) + 2 = A000079(n) + 3 = A000225(n) + 4 = A030101(A004119(n)) for n > 1.

G.f.: (4 - 7*x)/((1 - 2*x)*(1 - x)).

a(n) = A173921(A000051(n+1)). - Reinhard Zumkeller, Mar 04 2010

E.g.f.: exp(x)*(3 + exp(x)). - Stefano Spezia, May 06 2023