A116970 -id:A116970 - cp's OEIS frontend

A008344 a(1)=0; thereafter a(n+1) = a(n) - n if a(n) >= n otherwise a(n+1) = a(n) + n.

0, 1, 3, 0, 4, 9, 3, 10, 2, 11, 1, 12, 0, 13, 27, 12, 28, 11, 29, 10, 30, 9, 31, 8, 32, 7, 33, 6, 34, 5, 35, 4, 36, 3, 37, 2, 38, 1, 39, 0, 40, 81, 39, 82, 38, 83, 37, 84, 36, 85, 35, 86, 34, 87, 33, 88, 32, 89, 31, 90, 30, 91, 29, 92, 28, 93, 27, 94, 26, 95, 25, 96, 24, 97, 23, 98

Offset: 1

N. J. A. Sloane

p^a(n) = A084110(p^(n-1)) for n>1 and p prime. - Reinhard Zumkeller, May 12 2003
For n > 1: a(A029858(n)) = A029858(n) and a(A003462(n)) = 0. - Reinhard Zumkeller, May 09 2012
Absolute first differences of A085059; abs(a(n+1)-a(n)) = n, see also A086283. - Reinhard Zumkeller, Oct 17 2014
For n>3, when a(n) = 3, a(n+1) is in A116970. - Bill McEachen, Oct 03 2023

N. J. A. Sloane, Table of n, a(n) for n = 1..29524 (Up to the 10th 0 term)
Index entries for sequences related to Recamán's sequence

Cf. A046901, A008343, A088230, A085059, A086283.
Equals A085059(n)-1.
Cf. A076042 (based on squares).

a008344 n = a008344_list !! (n-1)
a008344_list = 0 : f 0 [1..] where
   f x (z:zs) = y : f y zs where y = if x < z then x + z else x - z
-- Reinhard Zumkeller, Oct 17 2014, May 08 2012

A008344 := proc(n) option remember; if n = 0 then 0 elif A008344(n-1) >= (n-1) then A008344(n-1)-(n-1) else A008344(n-1)+(n-1); fi; end;

a[1]=0; a[n_] := a[n]=If[a[n-1]>=n-1, a[n-1]-n+1, a[n-1]+n-1]
Transpose[ NestList[ If[First[#]>=Last[#],{First[#]-Last[#],Last[#]+1}, {First[#]+Last[#],Last[#]+1}]&,{0,1},80]][[1]] (* Harvey P. Dale, Jun 20 2011 *)
s = 0; Table[If[s < n, s = s + n, s = s - n], {n, 0, 80}] (* Horst H. Manninger, Dec 03 2018 *)

a(n) = my(expo = logint(2*n+1, 3), res = n - (3^expo-1)/2); if(res==0, 0, if(res%2, (3^expo-res)/2, 3^expo-1+res/2)) \\ Jianing Song, May 25 2021

This is a concatenation S_0, S_1, S_2, ... where S_i = [b_0, b_1, ..., b_{3^(i+1)-1}] with b_0 = 0, b_{2j-1} = k+1-j, b_{2j} = 2k+j (j=1..k), k=(3^(i+1)-1)/2. E.g. S_0 = [0, 1, 3], S_1 = [0, 4, 9, 3, 10, 2, 11, 1, 12].
a((3^n-1)/2) = 0; a((3^n-1)/2 + 2k-1) = (3^n+1)/2 - k for 1 <= k <= (3^n-1)/2; a((3^n-1)/2 + 2k) = 3^n - 1 + k for 1 <= k < (3^n-1)/2. - Benoit Cloitre, Jan 09 2003 [Corrected by Jianing Song, May 25 2021]
a(n) = (n-1+a(n-1)) mod (2*(n-1)). - Jon Maiga, Jul 09 2021

Name edited by Dmitry Kamenetsky, Feb 14 2017

A168613 a(n) = 3^n - 5.

Original entry on oeis.org

-4, -2, 4, 22, 76, 238, 724, 2182, 6556, 19678, 59044, 177142, 531436, 1594318, 4782964, 14348902, 43046716, 129140158, 387420484, 1162261462, 3486784396, 10460353198, 31381059604, 94143178822, 282429536476, 847288609438

Offset: 0

Vincenzo Librandi, Dec 01 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-3).

Cf. A168610.

I:=[-4, -2]; [n le 2 select I[n] else 4*Self(n-1)-3*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jul 06 2012

CoefficientList[Series[2*(7*x-2)/((1-x)*(1-3*x)),{x,0,40}],x] (* Vincenzo Librandi, Jul 06 2012 *)
LinearRecurrence[{4,-3}, {-4, -2}, 25] (* G. C. Greubel, Jul 27 2016 *)
3^Range[0,30]-5 (* Harvey P. Dale, Sep 12 2022 *)

a(n) = 3*a(n-1) + 10 with a(0)=-4.
G.f.: 2*(7*x - 2)/((1-x)*(1-3*x)). - Vincenzo Librandi, Jul 06 2012
a(n) = 4*a(n-1) - 3*a(n-2). - Vincenzo Librandi, Jul 06 2012
a(n) = 2*A116970(n) + 2 with A116970(0)=-3, A116970(1)=-2. - Bruno Berselli, Jul 06 2012
E.g.f.: exp(3*x) - 5*exp(x). - G. C. Greubel, Jul 27 2016

Formula and examples edited to use correct offset by Jon E. Schoenfield, Jun 19 2010

A063679 Numbers k such that (3^k - 7)/2 is prime.

Original entry on oeis.org

4, 12, 18, 26, 106, 164, 246, 956, 2554, 3350, 6496, 8706, 9008, 15398, 15490, 20408, 39240, 41060, 41842, 58358, 60346, 82214, 134972, 194014, 344204, 587712, 778070

Offset: 1

Jud McCranie, Jul 28 2001

x = 3^k is a solution to sigma(x - 7) = sigma(x) - 7 when (3^k - 7)/2 is prime.

a(28) > 10^6

			(3^4 - 7)/2 = 37 is prime, so 4 is in the sequence.

Cf. A000203, A063680, A015913-A015917, A054905, A116970.

with(numtheory):i := 0:x := 1:while i < 1000 do i := i+1:x := 3*x: if isprime((x-7)/2) then print(i):fi:od:

Do[ If[ PrimeQ[ (3^n - 7)/2 ], Print[n] ], {n, 2, 5500} ]
Select[Range[2, 10000], PrimeQ[((3^# - 7)/2)] &] (* Vincenzo Librandi, Sep 30 2012 *)

is(n)=ispseudoprime((3^n-7)/2) \\ Charles R Greathouse IV, May 22 2017

More terms from Robert G. Wilson v, Aug 02 2001
0, 1 removed and a(11)-a(13) added from Vincenzo Librandi, Sep 30 2012
a(14)-a(17) from Seth A. Troisi, Oct 17 2022
a(17) corrected, a(18)-a(25) from Seth A. Troisi, Oct 29 2022
a(26)-a(27) from Seth A. Troisi, Nov 28 2022

A277105 a(n) = (27*3^n - 63)/2.

Original entry on oeis.org

9, 90, 333, 1062, 3249, 9810, 29493, 88542, 265689, 797130, 2391453, 7174422, 21523329, 64570050, 193710213, 581130702, 1743392169, 5230176570, 15690529773, 47071589382, 141214768209, 423644304690, 1270932914133, 3812798742462, 11438396227449, 34315188682410, 102945566047293, 308836698141942, 926510094425889

Offset: 1

Emeric Deutsch, Nov 05 2016

a(n) is the second Zagreb index of the Hanoi graph H[n] (n>=2).
The second Zagreb index of a simple connected graph g is the sum of the degree products d(i)d(j) over all edges ij of g.
The M-polynomial of the Hanoi graph H[n] is  M(H[n],x,y) = 6*x^2*y^3 + (3/2)*(3^n - 5)*x^3*y^3.

E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
Eric Weisstein's World of Mathematics, Hanoi Graph
Index entries for linear recurrences with constant coefficients, signature (4,-3).

Cf. A116970, A277104.

[(27*3^n-63)/2: n in [1..30]]; // Bruno Berselli, Nov 14 2016

Maple
```
seq((1/2)*(9*(3^(n+1)-7)), n = 1..30);
```

Table[(27 3^n - 63)/2, {n, 1, 30}] (* Bruno Berselli, Nov 14 2016 *)

O.g.f.: 9*x*(1 + 6*x)/((1 - x)*(1 - 3*x)).
E.g.f.: 9*(1 - exp(x))*(4 - 3*exp(x) - 3*exp(2*x))/2. - Bruno Berselli, Nov 14 2016
a(n) = 9*A116970(n+1).

cp's OEIS Frontend

A008344 a(1)=0; thereafter a(n+1) = a(n) - n if a(n) >= n otherwise a(n+1) = a(n) + n.

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A168613 a(n) = 3^n - 5.

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A063679 Numbers k such that (3^k - 7)/2 is prime.

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Author

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Examples

Crossrefs

Programs

Maple

Mathematica

PARI

Extensions

A277105 a(n) = (27*3^n - 63)/2.

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Author

Keywords

Comments

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Crossrefs

Programs

Magma

Maple

Mathematica

Formula