A005849 -id:A005849 - cp's OEIS frontend

A128193 First differences of values of n for Cullen primes in A005849.

140, 4572, 1082, 816, 11885, 13796, 177, 27187, 31169, 171594, 98856, 120624, 872929, 4973720, 351333

Offset: 1

Enoch Haga, Feb 18 2007

Carlos Rivera's Problem 50 is devoted to this topic. If we pair differences according to magnitude, we first obtain 177-140=37 a prime. This raises the question as to whether there are other such prime values.

			a(1)=140 because the first pair of n are 1 and 141. 141 - 1 = 140.

Carlos Rivera, Problem 50. Is there a Cullen prime Cn with n prime?, The Prime Puzzles and Problems Connection.

Cf. A005849, A128194.

a(n) = A005849(n+1) - A005849(n). - Michel Marcus, Sep 27 2020

Offset 1 from Michel Marcus, Sep 27 2020

a(14)-a(15) added by Florian Baur, Sep 27 2020

A128194 Absolute value of second differences of A005849.

Original entry on oeis.org

4432, 3490, 266, 11069, 1911, 13619, 27010, 3982, 140425, 72738, 21768, 752305, 4100791, 4622387

Offset: 1

Enoch Haga, Feb 18 2007

In this sequence a(4) and a(6) are primes. Also a(2)+1, a(7)+1 and a(8)+1 are primes. And a(11)-1 is prime. These may at some future time begin three new sequences.

			a(1) = 4432 because the first two values of first differences in A128193 are 140 and 4572. 4572-140 = 4432, the first second difference.

Cf. A005849 A128193.

a(n) = abs(A128193(n+1) - A128193(n)). - Amiram Eldar, Jul 17 2025

Offset changed to 1, a(9)-a(10) corrected and a(13)-a(14) added by Amiram Eldar, Jul 17 2025

A002064 Cullen numbers: a(n) = n*2^n + 1.

Original entry on oeis.org

1, 3, 9, 25, 65, 161, 385, 897, 2049, 4609, 10241, 22529, 49153, 106497, 229377, 491521, 1048577, 2228225, 4718593, 9961473, 20971521, 44040193, 92274689, 192937985, 402653185, 838860801, 1744830465, 3623878657, 7516192769, 15569256449, 32212254721, 66571993089

Offset: 0

N. J. A. Sloane

Binomial transform is A084859. Inverse binomial transform is A004277. - Paul Barry, Jun 12 2003
Let A be the Hessenberg matrix of order n defined by: A[1,j]=1, A[i,i]:=2,(i>1), A[i,i-1] =-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n-1)= (-1)^(n-1)*coeff(charpoly(A,x),x). - Milan Janjic, Jan 26 2010
Indices of primes are listed in A005849. - M. F. Hasler, Jan 18 2015
Add the list of fractions beginning with 1/2 + 3/4 + 7/8 + ... + (2^n - 1)/2^n and take the sums pairwise from left to right. For 1/2 + 3/4 = 5/4, 5 + 4 = 9 = a(2); for 5/4 + 7/8 = 17/8, 17 + 8 = 25 = a(3); for 17/8 + 15/16 = 49/16, 49 + 16 = 65 = a(4); for 49/16 + 31/32 = 129/32, 129 + 32 = 161 = a(5). For each pairwise sum a/b, a + b = n*2^(n+1). - J. M. Bergot, May 06 2015
Number of divisors of (2^n)^(2^n). - Gus Wiseman, May 03 2021
Named after the Irish Jesuit priest James Cullen (1867-1933), who checked the primality of the terms up to n=100. - Amiram Eldar, Jun 05 2021

			G.f. = 1 + 3*x + 9*x^2 + 25*x^3 + 65*x^4 + 161*x^5 + 385*x^6 + 897*x^7 + ... - _Michael Somos_, Jul 18 2018

G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. p. 255.
R. K. Guy, Unsolved Problems in Number Theory, B20.
Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See pp. 240-242.
W. Sierpiński, Elementary Theory of Numbers. Państ. Wydaw. Nauk., Warsaw, 1964, p. 346.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n=0..300
Ray Ballinger, Cullen Primes: Definition and Status.
Attila Bérczes, István Pink, and Paul Thomas Young, Cullen numbers and Woodall numbers in generalized Fibonacci sequences, J. Num. Theor. (2024) Vol. 262, 86-102.
Yuri Bilu, Diego Marques, and Alain Togbé, Generalized Cullen numbers in linear recurrence sequences, Journal of Number Theory, Vol. 202 (2019), pp. 412-425; arXiv preprint, arXiv:1806.09441 [math.NT], 2018.
Daniel Birmajer, Juan B. Gil, David S. Kenepp, and Michael D. Weiner, Restricted generating trees for weak orderings, arXiv:2108.04302 [math.CO], 2021.
C. K. Caldwell, The Top Twenty: Cullen Primes.
James Cullen, Question 15897, Educational Times, Vol. 58 (December 1905), p. 534.
Orhan Eren and Yüksel Soykan, Gaussian Generalized Woodall Numbers, Arch. Current Res. Int'l (2023) Vol. 23, Iss. 8, Art. No. ACRI.108618, 48-68. See p. 50.
Orhan Eren and Yüksel Soykan, On Dual Hyperbolic Generalized Woodall Numbers, Archives Current Res. Int'l (2024) Vol. 24, Iss. 11, Art. No. ACRI.126420, 398-423. See p. 401.
Jon Grantham and Hester Graves, The abc Conjecture Implies That Only Finitely Many Cullen Numbers Are Repunits, arXiv:2009.04052 [math.NT], 2020.
José María Grau and Florian Luca, Cullen numbers with the Lehmer property, Proceedings of the American Mathematical Society, Vol. 140, No. 1 (2012), pp. 129-134; arXiv preprint, arXiv:1103.3578 [math.NT], Mar 18 2011.
Paul Leyland, Factors of Cullen and Woodall numbers.
Paul Leyland, Generalized Cullen and Woodall numbers.
Diego Marques, On Generalized Cullen and Woodall Numbers That are Also Fibonacci Numbers, Journal of Integer Sequences, Vol. 17 (2014), Article 14.9.4.
Hisanori Mishima, Factorizations of many number sequences, Cullen numbers (n = 1 to 100), (n = 101 to 200), (n = 201 to 300), (n = 301 to 323).
Simon Plouffe, Approximations de Séries Génératrices et Quelques Conjectures, Dissertation, Université du Québec à Montréal, 1992.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992.
Wacław Sierpiński, Elementary Theory of Numbers, Warszawa 1964.
Amelia Carolina Sparavigna, On the generalized sums of Mersenne, Fermat, Cullen and Woodall Numbers, Politecnico di Torino (Italy, 2019).
Amelia Carolina Sparavigna, Composition Operations of Generalized Entropies Applied to the Study of Numbers, International Journal of Sciences, Vol. 8, No. 4 (2019), pp. 87-92.
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, Vol. 8, No. 10 (2019).
Eric Weisstein's World of Mathematics, Cullen Number.
Wikipedia, Cullen number.
Index entries for linear recurrences with constant coefficients, signature (5,-8,4).

Cf. A005849, A003261, A050914, A130197, A134081, A001787, A143038, A156708, A181527.
Cf. A000325, A186947.
Diagonal k = n + 1 of A046688.
A000005 counts divisors of n.
A000312 = n^n.
A002109 gives hyperfactorials (sigma: A260146, omega: A303281).
A057156 = (2^n)^(2^n).
A062319 counts divisors of n^n.
A173339 lists positions of squares in A062319.
A188385 gives the highest prime exponent in n^n.
A249784 counts divisors of n^n^n.
Cf. A000169, A000272, A036289, A066959, A176029, A340841, A343656.

a002064 n = n * 2 ^ n + 1
a002064_list = 1 : 3 : (map (+ 1) $ zipWith (-) (tail xs) xs)
   where xs = map (* 4) a002064_list
-- Reinhard Zumkeller, Mar 16 2013

[n*2^n + 1: n in [0..40]]; // Vincenzo Librandi, May 07 2015

A002064:=-(1-2*z+2*z**2)/((z-1)*(-1+2*z)**2); # conjectured by Simon Plouffe in his 1992 dissertation

Table[n*2^n+1,{n,0,2*4!}] (* Vladimir Joseph Stephan Orlovsky, Apr 25 2010 *)
LinearRecurrence[{5,-8,4},{1,3,9},51] (* Harvey P. Dale, Oct 13 2011 *)
CoefficientList[Series[(1 - 2 x + 2 x^2)/((1 - x) (2 x - 1)^2), {x, 0, 50}], x] (* Vincenzo Librandi, May 07 2015 *)

A002064(n)=n*2^n+1  \\ M. F. Hasler, Oct 31 2012

a(n) = 4a(n-1) - 4a(n-2) + 1. - Paul Barry, Jun 12 2003
a(n) = sum of row (n+1) of triangle A130197. Example: a(3) = 25 = (12 + 8 + 4 + 1), row 4 of A130197. - Gary W. Adamson, May 16 2007
Row sums of triangle A134081. - Gary W. Adamson, Oct 07 2007
Equals row sums of triangle A143038. - Gary W. Adamson, Jul 18 2008
Equals row sums of triangle A156708. - Gary W. Adamson, Feb 13 2009
G.f.: -(1-2*x+2*x^2)/((-1+x)*(2*x-1)^2). a(n) = A001787(n+1)+1-A000079(n). - R. J. Mathar, Nov 16 2007
a(n) = 1 + 2^(n + log_2(n)) ~ 1 + A000079(n+A004257(n)). a(n) ~ A000051(n+A004257(n)). - Jonathan Vos Post, Jul 20 2008
a(0)=1, a(1)=3, a(2)=9, a(n) = 5*a(n-1)-8*a(n-2)+4*a(n-3). - Harvey P. Dale, Oct 13 2011
a(n) = A036289(n) + 1 = A003261(n) + 2. - Reinhard Zumkeller, Mar 16 2013
E.g.f.: 2*x*exp(2*x) + exp(x). - Robert Israel, Dec 12 2014
a(n) = 2^n * A000325(n) = 4^n * A186947(-n) for all n in Z. - Michael Somos, Jul 18 2018
a(n) = Sum_{i=0..n-1} a(i) + A000325(n+1). - Ivan N. Ianakiev, Aug 07 2019
a(n) = sigma((2^n)^(2^n)) = A000005(A057156(n)) = A062319(2^n). - Gus Wiseman, May 03 2021
Sum_{n>=0} 1/a(n) = A340841. - Amiram Eldar, Jun 05 2021

Edited by M. F. Hasler, Oct 31 2012

A003261 Woodall (or Riesel) numbers: n*2^n - 1.

Original entry on oeis.org

1, 7, 23, 63, 159, 383, 895, 2047, 4607, 10239, 22527, 49151, 106495, 229375, 491519, 1048575, 2228223, 4718591, 9961471, 20971519, 44040191, 92274687, 192937983, 402653183, 838860799, 1744830463, 3623878655, 7516192767, 15569256447, 32212254719, 66571993087

Offset: 1

N. J. A. Sloane

For n>1, a(n) is base at which zero is reached for the function "write f(j) in base j, read as base j+1 and then subtract 1 to give f(j+1)" starting from f(n) = n^2 - 1. - Henry Bottomley, Aug 06 2000

Sequence corresponds also to the maximum chain length of the classic puzzle whereby, under agreed commercial terms, an asset of unringed golden chain, when judiciously fragmented into as few as n pieces and n-1 opened links (through n-1 cuts), might be used to settle debt sequentially, with a golden link covering for unit cost. Here beside the n-1 opened links, the n fragmented pieces have lengths n, 2*n, 4*n, ..., 2^(n-1)*n. For instance, the chain of original length a(5)=159, if segregated by 4 cuts into 5+1+10+1+20+1+40+1+80, may be used to pay sequentially, i.e., a link-cost at a time, for an equivalent cost up to 159 links, to the same creditor. - Lekraj Beedassy, Feb 06 2003

			G.f. = x + 7*x^2 + 23*x^3 + 63*x^4 + 159*x^5 + 383*x^6 + 895*x^7 + ... - _Michael Somos_, Nov 04 2018

A. Brousseau, Number Theory Tables. Fibonacci Association, San Jose, CA, 1973, p. 159.
K. R. Bhutani and A. B. Levin, "The Problem of Sawing a Chain", Journal of Recreational Mathematics 2002-3 31(1) 32-35.
G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. p. 255.
M. Gardner, Martin Gardner's Sixth Book of Mathematical Diversions from Scientific American, "Gold Links", Problem 4, pp. 50-51; 57-58, University of Chicago Press, 1983.
O. O'Shea, Mathematical Brainteasers with Surprising Solutions, Problem 76, pp. 183-185, Prometheus Books, Guilford, Connecticut, 2020.
Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 241.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Vladimir Pletser, Table of n, a(n) for n = 1..3000 (terms 1..300 from T. D. Noe).
Ray Ballinger, Woodall Primes: Definition and Status.
Attila Bérczes, István Pink, and Paul Thomas Young, Cullen numbers and Woodall numbers in generalized Fibonacci sequences, J. Num. Theor. (2024) Vol. 262, 86-102.
Alfred Brousseau, Fibonacci and Related Number Theoretic Tables, Fibonacci Association, San Jose, CA, 1972. See p. 159.
C. K. Caldwell, Woodall Numbers.
Orhan Eren and Yüksel Soykan, Gaussian Generalized Woodall Numbers, Arch. Current Res. Int'l (2023) Vol. 23, Iss. 8, Art. No. ACRI.108618, 48-68. See p. 50.
Orhan Eren and Yüksel Soykan, On Dual Hyperbolic Generalized Woodall Numbers, Arch. Current Res. Int'l (2024) Vol. 24, Iss. 11, Art. No. ACRI.126420, 398-423. See p. 401.
Ignas Gasparavičius, Andrius Grigutis, and Juozas Petkelis, Picturesque convolution-like recurrences and partial sums' generation, arXiv:2507.23619 [math.NT], 2025. See p. 27.
Paul Leyland, Factors of Cullen and Woodall numbers.
Paul Leyland, Generalized Cullen and Woodall numbers.
D. Marques, On Generalized Cullen and Woodall Numbers That are Also Fibonacci Numbers, Journal of Integer Sequences, 17 (2014), #14.9.4.
Hisanori Mishima, Factorizations of many number sequences: Riesel numbers, n=1..100, n=101..200, n=201..300, n=301..323.
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992.
T. Sillke, Using Chains Links To Pay For A Room.
Amelia Carolina Sparavigna, On the generalized sums of Mersenne, Fermat, Cullen and Woodall Numbers, Politecnico di Torino (Italy, 2019).
Amelia Carolina Sparavigna, Composition Operations of Generalized Entropies Applied to the Study of Numbers, International Journal of Sciences (2019) Vol. 8, No. 4, 87-92.
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.
Eric Weisstein's World of Mathematics, Woodall Number.
Wikipedia, Woodall number.
Index entries for linear recurrences with constant coefficients, signature (5,-8,4).

Cf. A002234, A002064, A005849, A050918, A006127.
a(n) = A036289(n) - 1 = A002064(n) - 2.
Cf. A133653.

a003261 = (subtract 1) . a036289  -- Reinhard Zumkeller, Mar 05 2012

[n*2^n - 1: n in [1..30]]; // G. C. Greubel, Nov 04 2018

for n from 1 to 3000 do n, n*2^n -1; end do; # Vladimir Pletser, Dec 30 2022

Table[n*2^n-1,{n,3*4!}] (* Vladimir Joseph Stephan Orlovsky, Apr 25 2010 *)
LinearRecurrence[{5,-8,4},{1,7,23},30] (* Harvey P. Dale, Mar 13 2022 *)

A003261(n)=n*2^n-1  \\ M. F. Hasler, Oct 31 2012

[n*2**n - 1 for n in range(1, 29)] # Michael S. Branicky, Jan 07 2021

G.f.: x*(-1-2*x+4*x^2) / ( (x-1)*(-1+2*x)^2 ). - Simon Plouffe in his 1992 dissertation
Binomial transform of A133653 and double binomial transform of [1, 5, -1, 1, -1, 1, ...]. - Gary W. Adamson, Sep 19 2007
a(n) = -(2)^n * A006127(-n) for all n in Z. - Michael Somos, Nov 04 2018
E.g.f.: 1 + exp(x)*(2*exp(x)*x - 1). - Stefano Spezia, Nov 24 2024

A002234 Numbers k such that the Woodall number k*2^k - 1 is prime.

Original entry on oeis.org

2, 3, 6, 30, 75, 81, 115, 123, 249, 362, 384, 462, 512, 751, 822, 5312, 7755, 9531, 12379, 15822, 18885, 22971, 23005, 98726, 143018, 151023, 667071, 1195203, 1268979, 1467763, 2013992, 2367906, 3752948, 17016602

Offset: 1

N. J. A. Sloane, Simon Plouffe

a(34) = 17016602 is tentative until the range 16838832..17016601 is fully searched. - Eric W. Weisstein, Mar 22 2018

J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 115, p. 40, Ellipses, Paris 2008.
R. K. Guy, Unsolved Problems in Number Theory, Springer, 1st edition, 1981. See section B20.
F. Le Lionnais, Les Nombres Remarquables, Paris, Hermann, 1983, p. 95, 1983.
Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See pp. 241-242.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 139.

Ray Ballinger, Woodall Primes: Definition and Status.
Ray Ballinger and Wilfrid Keller, Woodall numbers.
C. K. Caldwell, Woodall Numbers.
J. DeMaio, Generalized Woodall Numbers.
Brady Haran and Matt Parker, 383 is cool, Numberphile video (2017).
R. Ondrejka, The Top Ten: a Catalogue of Primal Configurations.
PrimeGrid, PrimeGrid Primes: Subproject: (WOO) Woodall Prime Search.
Matt Parker and Brady Haran, 383 and Woodall Primes, Numberphile video (2017).
H. Riesel, Lucasian criteria for the primality of N=h.2^n-1, Math. Comp., 23 (1969), 869-875.
Eric Weisstein's World of Mathematics, Woodall Number.
Eric Weisstein's World of Mathematics, Integer Sequence Primes.

Cf. A050918 (for the actual primes), A003261, A005849.

is(n)=isprime(n<Charles R Greathouse IV, Feb 07 2017

a(27) communicated by Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 15 2004
a(28) = 1195203 found by M. Rodenkirch; contributed by Eric W. Weisstein, Nov 29 2005
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008
a(30)-a(33) from John Blazek, May 14 2009
a(34) = 17016602 communicated by Eric W. Weisstein, Mar 22 2018

A086661 Numbers k such that k*4^k-1 is prime.

Original entry on oeis.org

1, 2, 3, 5, 8, 14, 23, 63, 107, 132, 428, 530, 1137, 1973, 2000, 7064, 20747, 79574, 113570, 293912, 1993191

Offset: 1

Farideh Firoozbakht, Jul 27 2003

2, 3, 5, 23, 107, 1973, 20747 is the subsequence of prime terms.

			2 is in the sequence because 2*4^2-1=31 is prime.
3 is in the sequence because 3*4^3-1=191 is prime.

H. Dubner, Generalized Cullen Numbers, J. Rec. Math, 21 (No. 3, 1989).

Steven Harvey, Generalized Woodall Search

Cf. A007646, A002234, A005849.

Do[If[PrimeQ[n*4^n-1], Print[n]], {n, 4000}]
Select[Range[2000],PrimeQ[# 4^#-1]&] (* Harvey P. Dale, Nov 09 2024 *)

is(n)=ispseudoprime(n*4^n-1) \\ Charles R Greathouse IV, May 22 2017

One more term from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Nov 23 2004
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008
Prepended first terms 1 and 2 - Pierre CAMI, Jul 21 2014
a(20)-a(21) from Harvey link by Ray Chandler, Apr 10 2016

A058780 Numbers n such that n^2 * 2^n + 1 is prime.

Original entry on oeis.org

1, 2, 3, 4, 21, 30, 33, 57, 100, 142, 144, 150, 198, 225, 304, 513, 782, 858, 3638, 6076, 9297, 11037, 12135, 12876, 30180, 48470

Offset: 1

Robert G. Wilson v, Jan 02 2001

nonn

Steven Harvey, Generalized HyperCullen Primes

Cf. A282400, A058781, A005849.

Do[ If[ PrimeQ[ n^2*2^n + 1 ], Print[n] ], {n, 1, 5000} ]

is(n)=ispseudoprime(n^2*2^n+1) \\ Charles R Greathouse IV, May 22 2017

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008

A242176 Numbers k such that k*6^k + 1 is prime.

Original entry on oeis.org

1, 2, 91, 185, 387, 488, 747, 800, 9901, 10115, 12043, 13118, 30981, 51496

Offset: 1

Vincenzo Librandi, May 08 2014

G. Loeh, Generalized Cullen primes

Cf. numbers n such that n*k^n + 1 is prime: A005849 (k=2), A006552 (k=3), A007646 (k=4), this sequence (k=6), A242177 (k=7), A242178 (k=8), A007647 (k=10), A242196 (k=12), A242197 (k=14), A242198 (k=15), A242199 (k=16), A007648 (k=18).

[n: n in [0..1500] | IsPrime(n*6^n+1)];

Select[Range[1500], PrimeQ[# 6^# + 1] &]

is(n)=ispseudoprime(n*6^n+1) \\ Charles R Greathouse IV, Feb 17 2017

a(9)-a(14) from Loeh's list (see Links) - Bruno Berselli, May 08 2014

A006552 Numbers k such that k*3^k + 1 is prime.

Original entry on oeis.org

2, 8, 32, 54, 114, 414, 1400, 1850, 2848, 4874, 7268, 19290, 337590, 1183414

Offset: 1

N. J. A. Sloane

H. Dubner, Generalized Cullen numbers, J. Rec. Math., 21 (No. 3, 1989), 190-191.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

H. Dubner, Generalized Cullen numbers, J. Rec. Math., 21 (No. 3, 1989), 190-191. (Annotated scanned copy)
G. Loeh, Generalized Cullen primes

[n: n in [0..420] | IsPrime(n*3^n+1)]; // Vincenzo Librandi, Dec 02 2015

Select[Range[10000], PrimeQ[# 3^# + 1] &] (* Vincenzo Librandi, Dec 02 2015 *)

is(n)=ispseudoprime(n*3^n+1) \\ Charles R Greathouse IV, Feb 17 2017

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 05 2008

a(14) from Loeh link by Ray Chandler, Apr 10 2016

A050920 Cullen primes: primes of the form n*2^n+1.

Original entry on oeis.org

3, 393050634124102232869567034555427371542904833

Offset: 1

N. J. A. Sloane, Dec 30 1999

The next term is too large to display here, having 1423 digits. See A005849.

			1 * 2^1 + 1 = 3, which is prime.
141 * 2^141 + 1 = 393050634124102232869567034555427371542904833, which is also prime.
The third Cullen prime is approximately 2.677114856136697933736444 * 10^1422.

R. K. Guy, Unsolved Problems in Number Theory, Springer, 1st edition, 1981. See section B20.

Ray Ballinger, Cullen Primes: Definition and Status.
Chris K. Caldwell, Cullen Primes.
Eric Weisstein's World of Mathematics, Cullen Number.

See A005849 for the corresponding n.

Cf. A002064.

Select[Table[n * 2^n + 1, {n, 5000}], PrimeQ] (* Harvey P. Dale, Dec 14 2014 *)

a(n) = A002064(A005849(n)).

cp's OEIS Frontend

A128193 First differences of values of n for Cullen primes in A005849.

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A128194 Absolute value of second differences of A005849.

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A002064 Cullen numbers: a(n) = n*2^n + 1.

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A003261 Woodall (or Riesel) numbers: n*2^n - 1.

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A002234 Numbers k such that the Woodall number k*2^k - 1 is prime.

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A086661 Numbers k such that k*4^k-1 is prime.

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A058780 Numbers n such that n^2 * 2^n + 1 is prime.

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