A010712 -id:A010712 - cp's OEIS frontend

A047892 a(1) = 2; for n > 0, a(n+1) = a(n) * sum of digits of a(n).

2, 4, 16, 112, 448, 7168, 157696, 5361664, 166211584, 5651193856, 276908498944, 19383594926080, 1298700860047360, 79220752462888960, 6733763959345561600, 592571228422409420800, 45035413360103115980800

Offset: 1

Miklos SZABO (mike(AT)ludens.elte.hu)

a(n) mod 9 = A010712(n-1) for n > 1. - Reinhard Zumkeller, Sep 23 2007

Reinhard Zumkeller, Table of n, a(n) for n = 1..250

Cf. A004207.
Cf. A007953.
Cf. A047912 (start=3), A047897 (start=5), A047898 (start=6), A047899 (start=7), A047900 (start=8), A047901 (start=9), A047902 (start=11).

a047892 n = a047892_list !! (n-1)
a047892_list = iterate a057147 2  -- Reinhard Zumkeller, Mar 19 2014

NestList[# Total[IntegerDigits[#]]&,2,20] (* Harvey P. Dale, Jul 18 2011 *)

a(n+1) = A057147(a(n)). - Reinhard Zumkeller, Mar 19 2014

Offset changed by Reinhard Zumkeller, Mar 19 2014

A010691 Period 2: repeat (1,10).

Original entry on oeis.org

1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10, 1, 10

Offset: 0

N. J. A. Sloane

Regular continued fraction of (5+sqrt 35)/10. - R. J. Mathar, Nov 21 2011

Sequence is an infinite palindrome in two ways (numbers and English names): ONE, TEN, ONE, TEN, ONE, TEN, ONE, ... . - Eric Angelini, Sep 16 2023

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,1).

Cf. A036117, A070341, A168429, A070367, A070392, A070404, A048271, A187466.

[10^n mod 11: n in [0..80]]; // Vincenzo Librandi, Aug 24 2011

g:=(1+10*z)/((1-z^2)): gser:=series(g, z=0, 66): seq((coeff(gser, z, n)), n=0..65); # Zerinvary Lajos, Feb 25 2009

PadRight[{},100,{1,10}] (* Harvey P. Dale, Aug 27 2013 *)

a(n) = -9/2*(-1)^n + 11/2.
G.f.: (1+10*z)/(1-z^2). - Zerinvary Lajos, Feb 25 2009
a(n) = 10^n mod 11. - M. F. Hasler, Mar 10 2011
From Nicolas Bělohoubek, Nov 11 2021: (Start)
a(n) = 10/a(n-1). See also A010695.
a(n) = 11 - a(n-1). See also A010712. (End)

A176217 Decimal expansion of (14+4*sqrt(14))/7.

Original entry on oeis.org

4, 1, 3, 8, 0, 8, 9, 9, 3, 5, 2, 9, 9, 3, 9, 5, 0, 7, 7, 4, 7, 6, 4, 2, 7, 8, 4, 7, 0, 3, 8, 0, 2, 8, 1, 7, 2, 4, 3, 2, 0, 1, 1, 3, 1, 8, 7, 3, 0, 7, 0, 1, 1, 1, 2, 1, 7, 3, 5, 6, 8, 8, 3, 8, 4, 6, 8, 5, 9, 1, 5, 1, 7, 8, 8, 9, 6, 7, 9, 4, 4, 4, 5, 5, 8, 1, 7, 7, 0, 8, 2, 9, 6, 8, 2, 1, 6, 8, 9, 8, 0, 0, 0, 5, 6

Offset: 1

Klaus Brockhaus, Apr 12 2010

Continued fraction expansion of (14+4*sqrt(14))/7 is A010712.

			(14+4*sqrt(14))/7 = 4.13808993529939507747...

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A010471 (decimal expansion of sqrt(14)), A010712 (repeat 4, 7).

RealDigits[(14+4Sqrt[14])/7,10,120][[1]] (* Harvey P. Dale, Jan 24 2015 *)

A135541 a(n) = 2a(n-1) - a(n-2) + 2a(n-3), with a(0) = 2, a(1) = 2.

Original entry on oeis.org

0, 2, 7, 12, 21, 44, 91, 180, 357, 716, 1435, 2868, 5733, 11468, 22939, 45876, 91749, 183500, 367003, 734004, 1468005, 2936012, 5872027, 11744052, 23488101, 46976204, 93952411, 187904820, 375809637, 751619276, 1503238555, 3006477108

Offset: 0

Paul Curtz, Feb 22 2008

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,-1,2).

Cf. A007909, A007910, A010712, A016029, A134658.

I:=[0, 2, 7]; [n le 3 select I[n] else 2*Self(n-1)-Self(n-2)+2*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jun 17 2012

LinearRecurrence[{2,-1,2},{0,2,7},40] (* Vincenzo Librandi, Jun 17 2012 *)

From R. J. Mathar, Feb 23 2008: (Start)
O.g.f.: -7/(5*(2x-1)) - (4x+7)/(5*(x^2+1)).
a(n) = (7*2^n - (-1)^floor(n/2)*A010712(n+1))/5. (End)
E.g.f.: (1/5)*(7*cosh(2*x) + 7*sinh(2*x) - 7*cos(x) - 4*sin(x)). - G. C. Greubel, Oct 18 2016

More terms from R. J. Mathar, Feb 23 2008

A171231 a(n) = (10*2^n + 3 - (-1)^n)/6.

Original entry on oeis.org

2, 4, 7, 14, 27, 54, 107, 214, 427, 854, 1707, 3414, 6827, 13654, 27307, 54614, 109227, 218454, 436907, 873814, 1747627, 3495254, 6990507, 13981014, 27962027, 55924054, 111848107, 223696214, 447392427, 894784854, 1789569707

Offset: 0

Paul Curtz, Dec 05 2009

From 14, the last 2 digits are of period 4: repeat [14, 27, 54, 07]. - Paul Curtz, Nov 22 2024

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,1,-2).

Cf. A000035, A000975, A048573, A136412 (1st bisection), 2*A136412 (2nd bisection).

Cf. A010712, A160113.

[( 10*2^n+3-(-1)^n )/6: n in [0..40]]; // Vincenzo Librandi, Aug 05 2011

LinearRecurrence[{2,1,-2},{2,4,7},40] (* Harvey P. Dale, Feb 11 2015 *)

a(n)=(10<Charles R Greathouse IV, Jul 07 2011

a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3), n >= 3.
a(n+1) - a(n) = A048573(n-1).
a(n) = 2*A000975(n+1) - 3*A000975(n-1).
a(n) - a(n-2) = 5*2^n.
a(n+1) - 2*a(n) = ((-1)^n-1)/2 = -A000035(n).
G.f.: ( 2-3*x^2 ) / ( (x-1)*(2*x-1)*(1+x) ). - R. J. Mathar, Jul 07 2011
a(n) = ceiling( (5/3)*(2^n) ). - Wesley Ivan Hurt, Jun 28 2013

Definition replaced by the Lava formula of 2009. Contents converted to formulas. - R. J. Mathar, Jul 07 2011

A176436 Decimal expansion of (7+2*sqrt(14))/2.

Original entry on oeis.org

7, 2, 4, 1, 6, 5, 7, 3, 8, 6, 7, 7, 3, 9, 4, 1, 3, 8, 5, 5, 8, 3, 7, 4, 8, 7, 3, 2, 3, 1, 6, 5, 4, 9, 3, 0, 1, 7, 5, 6, 0, 1, 9, 8, 0, 7, 7, 7, 8, 7, 2, 6, 9, 4, 6, 3, 0, 3, 7, 4, 5, 4, 6, 7, 3, 2, 0, 0, 3, 5, 1, 5, 6, 3, 0, 6, 9, 3, 9, 0, 2, 7, 9, 7, 6, 8, 0, 9, 8, 9, 5, 1, 9, 4, 3, 7, 9, 5, 7, 1, 5, 0, 0, 9, 9

Offset: 1

Klaus Brockhaus, Apr 19 2010

Continued fraction expansion of (7+2*sqrt(14))/2 is A010712 preceded by 7.

			(7+2*sqrt(14))/2 = 7.24165738677394138558...

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Cf. A010471 (decimal expansion of sqrt(14)), A010712 (repeat 4, 7).

cp's OEIS Frontend

A047892 a(1) = 2; for n > 0, a(n+1) = a(n) * sum of digits of a(n).

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A010691 Period 2: repeat (1,10).

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A176217 Decimal expansion of (14+4*sqrt(14))/7.

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A135541 a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3), with a(0) = 2, a(1) = 2.

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A171231 a(n) = (10*2^n + 3 - (-1)^n)/6.

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A176436 Decimal expansion of (7+2*sqrt(14))/2.

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A135541 a(n) = 2a(n-1) - a(n-2) + 2a(n-3), with a(0) = 2, a(1) = 2.