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A034474 a(n) = 5^n + 1. 53
2, 6, 26, 126, 626, 3126, 15626, 78126, 390626, 1953126, 9765626, 48828126, 244140626, 1220703126, 6103515626, 30517578126, 152587890626, 762939453126, 3814697265626, 19073486328126, 95367431640626, 476837158203126 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Numbers n for which the expression 5^n/(n-1) is an integer. - Paolo P. Lava, May 29 2006

a(n) is the deficiency of 3 * 5^n (see A033879). - Patrick J. McNab, May 28 2017

LINKS

T. D. Noe, Table of n, a(n) for n = 0..200

Amelia Carolina Sparavigna, The groupoids of Mersenne, Fermat, Cullen, Woodall and other Numbers and their representations by means of integer sequences, Politecnico di Torino, Italy (2019), [math.NT].

Amelia Carolina Sparavigna, Some Groupoids and their Representations by Means of Integer Sequences, International Journal of Sciences (2019) Vol. 8, No. 10.

Index entries for linear recurrences with constant coefficients, signature (6,-5).

FORMULA

a(n) = 5*a(n-1) - 4 = 6*a(n-1) - 5*a(n-2).

From Mohammad K. Azarian, Jan 02 2009: (Start)

G.f.: 1/(1-x) + 1/(1-5*x).

E.g.f.: e^x + e^(5*x). (End)

a(n) = A279396(n+5,5). - Wolfdieter Lang, Jan 10 2017

EXAMPLE

G.f. = 2 + 6*x + 26*x^2 + 126*x^3 + 626*x^4 + 3126*x^5 + 15626*x^6 + ...

MATHEMATICA

Table[5^n + 1, {n, 0, 25}]

LinearRecurrence[{6, -5}, {2, 6}, 30] (* Harvey P. Dale, Jul 29 2015 *)

PROG

(Sage) [lucas_number2(n, 6, 5) for n in range(25)] # Zerinvary Lajos, Jul 08 2008

(Sage) [sigma(5, n) for n in range(25)] # Zerinvary Lajos, Jun 04 2009

(Sage) [5^n+1 for n in range(30)] # Bruno Berselli, Jan 11 2017

(PARI) a(n)=5^n+1 \\ Charles R Greathouse IV, Sep 24 2015

(MAGMA) [5^n+1: n in [0..30]]; // Vincenzo Librandi, Jan 11 2017

CROSSREFS

Cf. A000051, A034472, A052539, A062394, A034491, A062395, A062396, A062397, A007689, A063376, A063481, A074600-A074624, A034524, A178248, A228081, A279396, A024049.

Sequence in context: A208034 A092880 A192808 * A306041 A123872 A230071

Adjacent sequences:  A034471 A034472 A034473 * A034475 A034476 A034477

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 28 06:26 EDT 2020. Contains 338048 sequences. (Running on oeis4.)