A060353 -id:A060353 - cp's OEIS frontend

A060352 a(n) = n*3^n - 1.

2, 17, 80, 323, 1214, 4373, 15308, 52487, 177146, 590489, 1948616, 6377291, 20726198, 66961565, 215233604, 688747535, 2195382770, 6973568801, 22082967872, 69735688019, 219667417262, 690383311397, 2165293113020, 6778308875543, 21182215236074, 66088511536553, 205891132094648

Offset: 1

Jason Earls, Mar 31 2001

Harry J. Smith, Table of n, a(n) for n = 1..200
Paul Leyland, Factors of Cullen and Woodall numbers
Paul Leyland, Generalized Cullen and Woodall numbers
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 (7,-15,9).

Cf. A060353.

Table[n*3^n-1,{n,50}] (* Vladimir Joseph Stephan Orlovsky, May 19 2011 *)
LinearRecurrence[{7,-15,9},{2,17,80},50] (* Harvey P. Dale, Dec 14 2012 *)

a(n) = { n*3^n - 1 } \\ Harry J. Smith, Jul 04 2009

G.f.: x*(2-3*x)*(1+3*x)/((1-x)*(1-3*x)^2). - Colin Barker, Apr 22 2012
a(n) = 7*a(n-1) - 15*a(n-2) + 9*a(n-3), a(1)=2, a(2)=17, a(3)=80. - Harvey P. Dale, Dec 14 2012
E.g.f.: 1 + exp(x)*(3*exp(2*x)*x - 1). - Stefano Spezia, Jan 05 2020

A182373 Positive integers k such that k*3^k - 2 is prime.

Original entry on oeis.org

3, 5, 7, 37, 45, 53, 179, 277, 721, 2087, 6197, 6317, 8775, 12781, 38943, 47273, 50507, 66693

Offset: 1

Patrick Devlin, Apr 26 2012

Similar to A060353, and to the Woodall primes, A050918. The next term in the sequence is unknown; if the sequence is infinite, the next term is greater than 5000.
a(15) > 30000. - Tyler NeSmith, Apr 22 2022
a(19) > 10^5. - Michael S. Branicky, Sep 22 2024

			79 = 3*3^3 - 2; 1213 = 5*3^5 - 2; 15307 = 7*3^7 - 2.

Cf. A050918, A060353.

#choose N large, then S is the desired set
f:=n->n*3^n - 2:
S:={}:
for n from 0 to N do if(isprime(f(n))) then S:=S union {n}: fi: od

Select[Range[2100], PrimeQ[#*3^# - 2] &] (* Jayanta Basu, Jun 01 2013 *)

for(n=1, 1e6, if(ispseudoprime(3^n*n - 2), print1(n, ", "))) \\ Altug Alkan, Dec 01 2015

a(11)-a(14) from Altug Alkan, Dec 01 2015
a(15)-a(17) from Michael S. Branicky, Apr 23 2023
a(18) from Michael S. Branicky, Sep 22 2024

A182374 Primes of the form n*3^n + 1.

Original entry on oeis.org

19, 52489, 59296646043258913, 3140085798164163223281069127, 281013956365219695455558985684629594690518822413326510467

Offset: 1

Patrick Devlin, Apr 26 2012

nonn

Similar to A060353, and to the Woodall primes A050918.

			19 = 2*3^2 + 1; 52489 = 8*3^8 + 1; a(3) = 32*3^32 + 1; a(4) = 54*3^54 + 1.

Cf. A060353, A050918.

#choose N large, then S is the desired set
f:=n->n*3^n + 1:
S:={}:
for n from 0 to N do if(isprime(f(n))) then S:=S union {f(n)}: fi: od

Select[Table[n*3^n + 1, {n, 0, 580}], PrimeQ] (* Jayanta Basu, Jun 01 2013 *)

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A060352 a(n) = n*3^n - 1.

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A182373 Positive integers k such that k*3^k - 2 is prime.

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A182374 Primes of the form n*3^n + 1.

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