A050915 -id:A050915 - cp's OEIS frontend

A050914 a(n) = n*3^n + 1.

1, 4, 19, 82, 325, 1216, 4375, 15310, 52489, 177148, 590491, 1948618, 6377293, 20726200, 66961567, 215233606, 688747537, 2195382772, 6973568803, 22082967874, 69735688021, 219667417264, 690383311399, 2165293113022, 6778308875545, 21182215236076, 66088511536555, 205891132094650

Offset: 0

N. J. A. Sloane, Dec 30 1999

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Jon Grantham and Hester Graves, The abc Conjecture Implies That Only Finitely Many Cullen Numbers Are Repunits, arXiv:2009.04052 [math.NT], 2020.
Paul Leyland, Factors of Cullen and Woodall numbers.
Paul Leyland, Generalized Cullen and Woodall numbers.
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 (7,-15,9).

Cf. A002064, A050915.

Equals A036290(n) + 1.

[ n*3^n+1: n in [0..20]]; // Vincenzo Librandi, Sep 16 2011

Table[n*3^n+1,{n,0,30}] (* or *) LinearRecurrence[{7,-15,9},{1,4,19},30] (* Harvey P. Dale, Nov 07 2012 *)

a(n)=n*3^n+1 \\ Charles R Greathouse IV, Oct 07 2015

From Colin Barker, Oct 14 2012: (Start)
a(n) = 7*a(n-1) - 15*a(n-2) + 9*a(n-3).
G.f.: -(6*x^2 - 3*x + 1)/((x-1)*(3*x-1)^2). (End)
E.g.f.: exp(x)*(3*x*exp(2*x) + 1). - Elmo R. Oliveira, Sep 09 2024

A064749 a(n) = n*11^n + 1.

Original entry on oeis.org

1, 12, 243, 3994, 58565, 805256, 10629367, 136410198, 1714871049, 21221529220, 259374246011, 3138428376722, 37661140520653, 448795257871104, 5316497670165375, 62658722541234766, 735195677817154577, 8592599484487994108, 100078511642860166659, 1162022718519876379530

Offset: 0

N. J. A. Sloane, Oct 19 2001

Vincenzo Librandi, Table of n, a(n) for n = 0..900
Paul Leyland, Factors of Cullen and Woodall numbers.
Paul Leyland, Generalized Cullen and Woodall numbers.
Index entries for linear recurrences with constant coefficients, signature (23,-143,121).

For a(n)=n*k^n+1: A000012 (k=0), A000027(n+1) (k=1), A002064 (k=2), A050914 (k=3), A050915 (k=4), A050916 (k=5), A050917 (k=6), A050919 (k=7), A064746 (k=8), A064747 (k=9), A064748 (k=10), this sequence (k=11), A064750 (k=12).

Cf. A064757.

[n*11^n+1: n in [0..20]]; // Vincenzo Librandi, Sep 16 2011

k:= 11; f:= gfun:-rectoproc({-1 - (k-1)*n + k*n*a(n-1) - (n-1)*a(n) = 0, a(0) = 1, a(1) = k+1}, a(n), remember): map(f, [$0..20]); # Georg Fischer, Feb 19 2021

a(n) = A064757(n) + 2 for n>=1. - Georg Fischer, Feb 19 2021
G.f.: -(110*x^2-11*x+1)/((x-1)*(11*x-1)^2). - Alois P. Heinz, Feb 19 2021
From Elmo R. Oliveira, May 03 2025: (Start)
E.g.f.: exp(x)*(1 + 11*x*exp(10*x)).
a(n) = 23*a(n-1) - 143*a(n-2) + 121*a(n-3). (End)

A242204 Numbers n such that n*4^n+1 is semiprime.

Original entry on oeis.org

2, 6, 8, 9, 13, 15, 25, 36, 37, 63, 66, 72, 73, 85, 205, 333, 430

Offset: 1

Vincenzo Librandi, May 10 2014

The semiprimes of this form are: 33, 24577, 524289, 2359297, 872415233, 16106127361, 28147497671065601, 170005193383307227693057, 698910239464707491627009, ...

a(18) >= 547. - Hugo Pfoertner, Aug 05 2019

factordb.com, Status of 547*4^547+1.

Cf. similar sequences listed in A242203.

Cf. A007646, A050915.

IsSemiprime:=func; [n: n in [1..110] | IsSemiprime(s) where s is n*4^n+1];

Mathematica

Select[Range[120], PrimeOmega[# 4^# + 1] == 2 &]

Extensions

a(15)-a(17) from Luke March, Aug 13 2015

cp's OEIS Frontend

A050914 a(n) = n*3^n + 1.

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A064749 a(n) = n*11^n + 1.

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A242204 Numbers n such that n*4^n+1 is semiprime.

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