A009990 -id:A009990 - cp's OEIS frontend

A009967 Powers of 23.

1, 23, 529, 12167, 279841, 6436343, 148035889, 3404825447, 78310985281, 1801152661463, 41426511213649, 952809757913927, 21914624432020321, 504036361936467383, 11592836324538749809, 266635235464391245607, 6132610415680998648961, 141050039560662968926103, 3244150909895248285300369, 74615470927590710561908487, 1716155831334586342923895201

Offset: 0

N. J. A. Sloane

Same as Pisot sequences E(1, 23), L(1, 23), P(1, 23), T(1, 23). Essentially same as Pisot sequences E(23, 529), L(23, 529), P(23, 529), T(23, 529). See A008776 for definitions of Pisot sequences.
The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n>=1, a(n) equals the number of 23-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011
Numbers k such that sigma(23*k) = 23*k + sigma(k). - Jahangeer Kholdi, Nov 23 2013

T. D. Noe, Table of n, a(n) for n = 0..100
Tanya Khovanova, Recursive Sequences.
Index entries for linear recurrences with constant coefficients, signature (23).

Cf. A000079, A008776, A009990.

[23^n: n in [0..100]]; // Vincenzo Librandi, Nov 21 2010

23^Range[0,20]  (* Harvey P. Dale, Apr 04 2011 *)

A009967(n):=23^n$
makelist(A009967(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

a(n)=23^n \\ Charles R Greathouse IV, Sep 24 2015

[lucas_number1(n,23,0) for n in range(1, 17)] # Zerinvary Lajos, Apr 29 2009

G.f.: 1/(1-23*x). - Philippe Deléham, Nov 23 2008
a(n) = 23^n; a(n) = 23*a(n-1) n>0 a(0)=1. - Vincenzo Librandi, Nov 21 2010
From Elmo R. Oliveira, Jul 10 2025: (Start)
E.g.f.: exp(23*x).
a(n) = A009990(n)/A000079(n). (End)

A218749 a(n) = (46^n - 1)/45.

Original entry on oeis.org

0, 1, 47, 2163, 99499, 4576955, 210539931, 9684836827, 445502494043, 20493114725979, 942683277395035, 43363430760171611, 1994717814967894107, 91757019488523128923, 4220822896472063930459, 194157853237714940801115, 8931261248934887276851291, 410838017451004814735159387

Offset: 0

M. F. Hasler, Nov 04 2012

Partial sums of powers of 46 (A009990).

Vincenzo Librandi, Table of n, a(n) for n = 0..600
Index entries related to partial sums.
Index entries related to q-numbers.
Index entries for linear recurrences with constant coefficients, signature (47,-46).

Cf. similar sequences of the form (k^n-1)/(k-1): A000225, A003462, A002450, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125, A091030, A135519, A135518, A131865, A091045, A218721, A218722, A064108, A218724-A218734, A132469, A218736-A218753, A133853, A094028, A218723.

Cf. A009990.

[n le 2 select n-1 else 47*Self(n-1) - 46*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 08 2012

LinearRecurrence[{47, -46}, {0, 1}, 30] (* Vincenzo Librandi, Nov 08 2012 *)
(46^Range[0,20]-1)/45 (* Harvey P. Dale, Aug 17 2017 *)

A218749(n):=(46^n-1)/45$ makelist(A218749(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

PARI
```
A218749(n)=46^n\45
```

From Vincenzo Librandi, Nov 08 2012: (Start)
G.f.: x/((1-x)*(1-46*x)).
a(n) = 47*a(n-1) - 46*a(n-2) with a(0)=0, a(1)=1.
a(n) = 46*a(n-1) + 1 with a(0)=0.
a(n) = floor(46^n/45). (End)
E.g.f.: exp(x)*(exp(45*x) - 1)/45. - Elmo R. Oliveira, Aug 29 2024

A165867 Totally multiplicative sequence with a(p) = 46.

Original entry on oeis.org

1, 46, 46, 2116, 46, 2116, 46, 97336, 2116, 2116, 46, 97336, 46, 2116, 2116, 4477456, 46, 97336, 46, 97336, 2116, 2116, 46, 4477456, 2116, 2116, 97336, 97336, 46, 97336, 46, 205962976, 2116, 2116, 2116, 4477456, 46, 2116, 2116, 4477456, 46, 97336, 46

Offset: 1

Jaroslav Krizek, Sep 28 2009

G. C. Greubel, Table of n, a(n) for n = 1..10000

46^PrimeOmega[Range[100]] (* G. C. Greubel, Apr 16 2016 *)

a(n) = 46^bigomega(n); \\ Altug Alkan, Apr 16 2016

a(n) = A009990(A001222(n)) = 46^bigomega(n) = 46^A001222(n).

cp's OEIS Frontend

A009967 Powers of 23.

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A218749 a(n) = (46^n - 1)/45.

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A165867 Totally multiplicative sequence with a(p) = 46.

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Author

Keywords

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Programs

Mathematica

PARI

Formula