A195744 a(n) = 15*2^(n+1) + 1.

31, 61, 121, 241, 481, 961, 1921, 3841, 7681, 15361, 30721, 61441, 122881, 245761, 491521, 983041, 1966081, 3932161, 7864321, 15728641, 31457281, 62914561, 125829121, 251658241, 503316481, 1006632961, 2013265921, 4026531841, 8053063681, 16106127361

Offset: 0

Author

Brad Clardy, Sep 23 2011

Keywords

• easy
• nonn

Comments

Binary numbers of form 1111(0^n)1 where n is the index and number of 0's.

Base 10 numbers of this sequence always end in 1.

An Engel expansion of 1/15 to the base 2 as defined in A181565, with the associated series expansion 1/15 = 2/31 + 2^2/(31*61) + 2^3/(31*61*121) + 2^4/(31*61*121*241) + ... . - Peter Bala, Oct 29 2013

The only squares in this sequence are 121 = 11^2 and 961 = 31^2. - Antti Karttunen, Sep 24 2023

Examples

			First few terms in binary are 11111, 111101, 1111001, 11110001, 111100001.
		

Links

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

Crossrefs

Cf. A052996, A164094.

Cf. A020737, A083575, A083683, A083686, A083705, A168596, A181565.

Cf. A110286, A128470.

Cf. A005940, A030514.

Programs

Magma

[15*2^(n+1) + 1: n in [0..30]]; // Vincenzo Librandi, Sep 24 2011

Mathematica

15*2^Range[50] + 1 (* Paolo Xausa, Apr 02 2024 *)

PARI

a(n)=30*2^n+1 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = A052996(n+3) + A164094(n+2).

From Bruno Berselli, Sep 23 2011: (Start)

G.f.: (31-32*x)/(1-3*x+2*x^2).

a(n) = 2*a(n-1)-1.

a(n) = A110286(n+1)+1 = A128470(2^n). (End)

E.g.f.: exp(x)*(1 + 30*exp(x)). - Stefano Spezia, Oct 08 2022

For n >= 0, A005940(a(n)) = A030514(2+n). - Antti Karttunen, Sep 24 2023

Extensions

Corrected by Arkadiusz Wesolowski, Sep 23 2011