A178674 -id:A178674 - cp's OEIS frontend

A119626 Erroneous version of A178674.

6, 12, 30, 84, 246, 732, 2790, 8364, 25086, 75252, 225750, 677264

Offset: 1

dead

A168609 a(n) = 3^n + 4.

5, 7, 13, 31, 85, 247, 733, 2191, 6565, 19687, 59053, 177151, 531445, 1594327, 4782973, 14348911, 43046725, 129140167, 387420493, 1162261471, 3486784405, 10460353207, 31381059613, 94143178831, 282429536485, 847288609447

Offset: 0

Vincenzo Librandi, Dec 01 2009

			a(1)=3*5-8=7; a(2)=3*7-8=13; a(3)=3*13-8=31.

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

Cf. A034472, A168607, A168610, A178674.

[3^n+4: n in [0..30]]; // Vincenzo Librandi, May 13 2014

Table[3^n + 4, {n, 0, 50}] (* Vladimir Joseph Stephan Orlovsky, May 19 2011 *)
CoefficientList[Series[(5 - 13 x)/((1 - x) (1 - 3 x)), {x, 0, 30}], x] (* Vincenzo Librandi, May 13 2014 *)
LinearRecurrence[{4,-3},{5,7},30] (* Harvey P. Dale, Mar 11 2023 *)

a(n) = 3*a(n-1) - 8, with n>0, a(0)=5.
G.f.: (5 - 13*x)/((1-x)*(1-3 x)). - Vincenzo Librandi, May 13 2014
a(n) = 4*a(n-1) - 3*a(n-2) for n>1. - Vincenzo Librandi, May 13 2014
E.g.f.: exp(3*x) + 4*exp(x). - G. C. Greubel, Jul 27 2016

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

A178675 a(n) = 4^n + 4.

Original entry on oeis.org

5, 8, 20, 68, 260, 1028, 4100, 16388, 65540, 262148, 1048580, 4194308, 16777220, 67108868, 268435460, 1073741828, 4294967300, 17179869188, 68719476740, 274877906948, 1099511627780, 4398046511108, 17592186044420, 70368744177668, 281474976710660, 1125899906842628

Offset: 0

Vincenzo Librandi, Dec 25 2010

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-4).

Cf. A052548, A178674, A178676, A178681.

List([0..30], n -> 4^n + 4); # G. C. Greubel, Jan 27 2019

Magma
```
[4^n+4: n in [0..35]];
```

I:=[5, 8]; [n le 2 select I[n] else 5*Self(n-1)-4*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jun 18 2013

Table[4^n +4, {n, 0, 40}] (* or *) CoefficientList[Series[(5-17x)/((4x - 1)(x-1)), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 18 2013 *)
LinearRecurrence[{5,-4},{5,8},30] (* Harvey P. Dale, Sep 12 2023 *)

vector(40, n, n--; 4^n+4) \\ G. C. Greubel, Jan 27 2019

[4^n+4 for n in range(40)] # G. C. Greubel, Jan 27 2019

a(n) = 4*(a(n-1) - 3) with n > 0, a(0)=5.
G.f.: ( 5-17*x ) / ( (1-4*x)*(1-x) ). - R. J. Mathar, Jan 05 2011
a(n) = 5*a(n-1) - 4*a(n-2). - Vincenzo Librandi, Jun 18 2013
E.g.f.: exp(4*x) + 4*exp(x). - G. C. Greubel, Jan 27 2019

A301919 a(n) is the least value of k for which A301918(n) divides 3^k+3.

Original entry on oeis.org

0, 1, 3, 4, 9, 10, 15, 16, 10, 5, 22, 27, 6, 12, 7, 40, 45, 25, 51, 18, 57, 64, 69, 70, 75, 26, 40, 82, 87, 9, 99, 100, 106, 112, 117, 61, 129, 135, 16, 141, 142, 147, 18, 159, 166, 85, 88, 177, 62, 94, 190, 195, 100, 201, 103, 74, 225, 115, 231, 232, 244, 84

Offset: 1

Luke W. Richards, Mar 28 2018

nonn

This can be used to identify P+1 values to primality test potential primes P of the form 3^k+2, i.e., A051783.

			All values of 3^k+3 are multiples of 2, so 3^0+3 = 4 is the least value of k which is a multiple of 2.
a(10) = 5 and A301918(10) = 41 so 3^5+3 = 246 is the first multiple of 41 which can be written in the form 3^k+3.

Cf. A051783, A178674, A301916, A301917, A301918.

a(n) = A301917(n-1) + 1 for n > 2.

A161720 a(n) = (prime(n) - 7)/2.

Original entry on oeis.org

-1, 0, 2, 3, 5, 6, 8, 11, 12, 15, 17, 18, 20, 23, 26, 27, 30, 32, 33, 36, 38, 41, 45, 47, 48, 50, 51, 53, 60, 62, 65, 66, 71, 72, 75, 78, 80, 83, 86, 87, 92, 93, 95, 96, 102, 108, 110, 111, 113, 116, 117, 122, 125, 128, 131, 132

Offset: 3

G. A. Isa (isaabor(AT)yahoo.com), Jun 18 2009

Original name was: Half the difference between the first and the last numbers in the 7th circle of the cyclic representation of some structures whose cardinality generates Aminu numbers.

A bijective operator is defined on the Aminu numbers which in turn generates another cyclic group. Aminu numbers were first reported as the cardinality of some subgroups of regular groups whose order and degree coincide (Ibrahim,2004;2005;2007 and Ibrahim and Audu 2005). The action of the operator on the group structures where constructed using some special succession scheme which led to sequences such as A005097. This sequence enumerates half the difference between the first and last numbers in the 7th cycle of such group structures.

			For Pn=5, a(1)=-2/2=-1, for Pn=7, a(2)=0/2=0, for Pn=11,a(3)=4/2=2

A. A. Ibrahim, Group theoretic interpretation of Bara'a al-Dhimmah Models: Proceedings of Annual National Conference of Mathematical Association of Nigeria, MAN,(2004), 35-40.
A. A. Ibrahim and M. S. Audu, Some Group Theoretic Properties of Certain class of (123) and (132)- Avoiding Patterns of numbers: An enumeration scheme,African Journal of Natural Sciences, 8(1)(2005), 79-84.
A. A. Ibrahim, An Enumeration scheme and Algebraic properties of a special (132)- avoiding class of permutations Patterns, Trends in Applied sciences Research, Academic Journal Inc. 2(4)(2007), 334-340.

Cf. A178674, A000040, A005097.

Essentially a duplicate of A105760.

a(n)=(prime(n)-7)/2 \\ Charles R Greathouse IV, Jun 15 2013

a(n) = A105760(n-3). - R. J. Mathar, Sep 11 2012

Name changed by Arkadiusz Wesolowski, Jun 15 2013

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A119626 Erroneous version of A178674.

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A168609 a(n) = 3^n + 4.

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A178675 a(n) = 4^n + 4.

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A301919 a(n) is the least value of k for which A301918(n) divides 3^k+3.

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A161720 a(n) = (prime(n) - 7)/2.

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