A156940 -id:A156940 - cp's OEIS frontend

A243429 Primes of the form 2^n + 39.

41, 43, 47, 71, 103, 167, 1063, 2087, 8231, 131111, 536870951, 8589934631, 549755813927, 8796093022247, 154742504910672534362390567, 40564819207303340847894502572071, 162259276829213363391578010288167, 2722258935367507707706996859454145691687

Offset: 1

Vincenzo Librandi, Jun 05 2014

nonn

Associated n: 1, 2, 3, 5, 6, 7, 10, 11, 13, 17, 29, 33, 39, 43, 87, 105, 107, 131, 253, 329, ....

Vincenzo Librandi, Table of n, a(n) for n = 1..34

Cf. primes of the form 2^n+k: A092506 (k=1), A057733 (k=3), A123250 (k=5), A104066 (k=7), A104070 (k=9), A156940 (k=11), A104067 (k=13), A144487 (k=15), A156973 (k=17), A104068 (k=19), A156983 (k=21), A176922 (k=23), A104072 (k=25), A104071 (k=27), A156974 (k=29), A104069 (k=31), A176926 (k=33), A176927 (k=35), A176924 (k=37), this sequence (k=39), A176925 (k=41), A243430 (k=43), A243431 (k=45), A243432 (k=47), A104073 (k=49).

[a: n in [0..500] | IsPrime(a) where a is 2^n+39];

Select[Table[2^n + 39, {n, 0, 500}], PrimeQ]

A156973 Primes of the form 2^k + 17.

Original entry on oeis.org

19, 8209, 2097169, 8589934609, 2417851639229258349412369, 680564733841876926926749214863536422929, 62165404551223330269422781018352605012557018849668464680057997111644937126566671941649

Offset: 1

Edwin Dyke (ed.dyke(AT)btinternet.com), Feb 19 2009

nonn

			19 = 2^1 + 17 is in the sequence;
8209 = 2^13 + 17 is in the sequence.

Cf. A000040, A057200, A057733 (2^k + 3), A123250 (2^k + 5), A104066 (2^k + 7), A156940 (2^k + 11), A104067 (2^k + 13).

[ a: n in [1..400] | IsPrime(a) where a is 2^n+17 ]; // Vincenzo Librandi, Nov 27 2010

Delete[Union[Table[If[PrimeQ[2^n + 17], 2^n + 17, 0], {n, 1, 300}]],1]

a(n) = 2^A057200(n) + 17. - Elmo R. Oliveira, Nov 08 2023

a(7) from Vincenzo Librandi, Apr 29 2010

A156974 Primes of the form 2^k + 29.

Original entry on oeis.org

31, 37, 61, 157, 541, 8221, 32797, 131101, 8388637, 134217757, 8589934621, 137438953501, 8796093022237, 9223372036854775837, 590295810358705651741, 9444732965739290427421, 604462909807314587353117, 618970019642690137449562141, 166153499473114484112975882535043101, 170141183460469231731687303715884105757, 883423532389192164791648750371459257913741948437809479060803100646309917

Offset: 1

Edwin Dyke (ed.dyke(AT)btinternet.com), Feb 19 2009

nonn

Cf. A000040, A156982.

Cf. A057733 (2^k+3), A123250 (2^k+5), A104066 (2^k+7), A156940 (2^k+11).

[a: n in [0..300] | IsPrime(a) where a is 2^n+29 ]; // Vincenzo Librandi, Nov 27 2010

a := proc (n) if isprime(2^n+29) = true then 2^n+29 else end if end proc: seq(a(n), n = 1 .. 110); # Emeric Deutsch, Mar 14 2009

Delete[Union[Table[If[PrimeQ[2^n + 29], 2^n + 29, 0], {n, 1, 500}]],1]

a(n) = 2^A156982(n) + 29. - Elmo R. Oliveira, Nov 08 2023

More terms from Emeric Deutsch, Mar 14 2009

More terms from Vincenzo Librandi, Nov 27 2010

A172183 a(n) is the smallest prime of the form p^q+n, where p and q are prime, or zero if no such prime exists.

Original entry on oeis.org

5, 11, 7, 13, 13, 31, 11, 17, 13, 19, 19, 37, 17, 23, 19, 41, 8209, 43, 23, 29, 29, 31, 31, 73, 29, 53, 31, 37, 37, 79, 0, 41, 37, 43, 43, 61, 41, 47, 43, 67, 73, 67, 47, 53, 53, 71, 79, 73, 53, 59, 59, 61, 61, 79, 59, 83, 61, 67, 67, 109, 0, 71, 67, 73, 73, 191, 71, 193, 73, 79

Offset: 1

Cheng Zhang (cz1(AT)rice.edu), Jan 28 2010, Mar 02 2010

nonn

If n mod 6 = 1, both p and q must be 2, and a(n)=0 if n + 4 is not a prime. The values of a(n) for n=257,297,353,383,557 are either greater than 176 000 or 0. Several large entries: a(87) = 2^25633 + 87, a(717) = 2^3217 + 717, a(773) = 2^2539 + 773, a(927) = 2^1117 + 927.

			a(1)=5 because 5=2^2+1 is the smallest prime of the form p^q+1. a(2)=11 because 11=3^2+2. a(3)=7, because 7=2^2+3. a(17)=8209, because 8209=2^13+17. a(31)=0, because p^q+31 cannot be a prime.

Cf. A123318, A056208, A056206, A057733, A123250, A104066, A156940, A104067, A156973

For[l = {}; n = 1, n <= 70, n++, found = False; If[Mod[n, 2] == 0, For[rm = Infinity; i = 1, i < 100, i++, For[j = 1, j < 100, j++, p = Prime[i]; q = Prime[j]; r = p^q + n; If[r >= rm, Break[], If[PrimeQ[r], rm = r; found = True]]; ]; ], (* if n is odd, r=2^q+n *) If[Mod[n, 6] == 1, r = 4 + n; If[PrimeQ[r], found = True], For[j = 1, j < 1000, j++, q = Prime[j]; r = 2^q + n; If[PrimeQ[r], found = True; rm = r; Break[]]; ]; ]; ]; If[ ! found, rm = 0]; l = Append[l, rm]; ]; l

A267615 a(n) = 2^n + 11.

Original entry on oeis.org

12, 13, 15, 19, 27, 43, 75, 139, 267, 523, 1035, 2059, 4107, 8203, 16395, 32779, 65547, 131083, 262155, 524299, 1048587, 2097163, 4194315, 8388619, 16777227, 33554443, 67108875, 134217739, 268435467, 536870923, 1073741835, 2147483659, 4294967307, 8589934603, 17179869195, 34359738379

Offset: 0

Ilya Gutkovskiy, Jan 18 2016

Recurrence relation b(n) = 3*b(n - 1) - 2*b(n - 2) for n>1, b(0) = k, b(1) = k + 1, gives the closed form b(n) = 2^n + k - 1.

Index entries for linear recurrences with constant coefficients, signature (3,-2).

Cf. sequences with closed form 2^n + k - 1: A168616 (k=-4), A028399 (k=-3), A036563 (k=-2), A000918 (k=-1), A000225 (k=0), A000079 (k=1), A000051 (k=2), A052548 (k=3), A062709 (k=4), A140504 (k=5), A168614 (k=6), A153972 (k=7), A168415 (k=8), A242475 (k=9), A188165 (k=10), A246139 (k=11), this sequence (k=12).

Cf. A156940.

[2^n+11: n in [0..30]]; // Vincenzo Librandi, Jan 19 2016

Table[2^n + 11, {n, 0, 35}]
LinearRecurrence[{3, -2}, {12, 13}, 40] (* Vincenzo Librandi, Jan 19 2016 *)

a(n) = 2^n + 11; \\ Altug Alkan, Jan 18 2016

G.f.: (12 - 23*x)/(1 - 3*x + 2*x^2).
a(n) = 3*a(n - 1) - 2*a(n - 2) for n>1, a(0)=12, a(1)=13.
a(n) = A000079(n) + A010850(n).
Sum_{n>=0} 1/a(n) = 0.367971714327125...
Lim_{n->oo} a(n + 1)/a(n) = 2.
E.g.f.: exp(2*x) + 11*exp(x). - Elmo R. Oliveira, Nov 08 2023

cp's OEIS Frontend

A243429 Primes of the form 2^n + 39.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

A156973 Primes of the form 2^k + 17.

Views

Author

Keywords

Examples

Crossrefs

Programs

Magma

Mathematica

Formula

Extensions

A156974 Primes of the form 2^k + 29.

Views

Author

Keywords

Crossrefs

Programs

Magma

Maple

Mathematica

Formula

Extensions

A172183 a(n) is the smallest prime of the form p^q+n, where p and q are prime, or zero if no such prime exists.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A267615 a(n) = 2^n + 11.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula