A051783 -id:A051783 - cp's OEIS frontend

A219051 Numbers k such that 3^k - 34 is prime.

4, 7, 11, 13, 29, 32, 36, 44, 79, 157, 197, 341, 467, 996, 1421, 2479, 3269, 5203, 7987, 9341, 14836, 26047, 47816, 64304, 100693, 127597, 167167, 174697, 182089, 198791

Offset: 1

Nicolas M. Perrault, Nov 10 2012

a(31) > 2*10^5. - Robert Price, Nov 23 2013

			For k = 4, 3^4 - 34 = 47 and 47 is prime. Hence k = 4 is included in the sequence.

Cf. Sequences of numbers k such that 3^k + m is prime:
  (m = 2) A051783, (m = -2) A014224, (m = 4) A058958, (m = -4) A058959,
  (m = 8) A217136, (m = -8) A217135, (m = 10) A217137, (m = -10) A217347,
  (m = 14) A219035, (m = -14) A219038, (m = 16) A205647, (m = -16) A219039,
  (m = 20) A219040, (m = -20) A219041, (m = 22) A219042, (m = -22) A219043,
  (m = 26) A219044, (m = -26) A219045, (m = 28) A219046, (m = -28) A219047,
  (m = 32) A219048, (m = -32) A219049, (m = 34) A219050, (m = -34) A219051. Note that if m is a multiple of 3, 3^k + m is also a multiple of 3 (for k greater than 0), and as such isn't prime.

Do[If[PrimeQ[3^n - 34], Print[n]], {n, 1, 10000}]
Select[Range[10000], PrimeQ[3^# - 34] &] (* Alonso del Arte, Nov 10 2012 *)

is(n)=isprime(3^n-34) \\ Charles R Greathouse IV, Feb 17 2017

a(21)-a(30) from Robert Price, Nov 23 2013

A087885 Numbers k such that 5^k + 2 is a prime.

Original entry on oeis.org

0, 1, 3, 17, 143, 261, 551, 2285, 18731, 18995, 19751, 62067, 98051, 169727, 442281

Offset: 1

Donald S. McDonald, Oct 13 2003

Terms <= 551 correspond to certified primes.

a(15) > 2*10^5. - Robert Price, Jan 16 2015

			a(3)=3 is a term because 5^3 + 2 = 127 is a prime.
5^17 + 2 = 762939453127 is prime, hence 17 is a term.

Henri & Renaud Lifchitz, PRP Records.

Cf. A051783 (3^n + 2 is prime).

Do[If[PrimeQ[5^n + 2], Print[n]], {n, 1, 10000}] (* Ryan Propper, Jun 17 2005 *)

for(n=0, 10^5, if(ispseudoprime(5^n+2), print1(n, ", "))) \\ Felix Fröhlich, Jun 04 2014

a(7)-a(8) from Ryan Propper, Jun 17 2005
a(9)-a(12) found by Mike Oakes in 2003. - Alexander Adamchuk, Mar 02 2008
Edited by Ray Chandler, Jul 27 2011
a(13) from Ray Chandler, Jul 28 2011
a(14) from Robert Price, Jan 16 2015
a(15) from Paul Bourdelais, Jan 28 2021

A090649 Numbers k such that 9^k + 2 is prime.

Original entry on oeis.org

0, 1, 2, 4, 5, 7, 12, 13, 18, 49, 55, 63, 193, 247, 610, 929, 2173, 3479, 5494, 11158, 16754, 30920, 47752, 50702, 53725, 68122, 89214, 180804

Offset: 1

Herman H. Rosenfeld (herm3(AT)pacbell.net), Feb 02 2004

All terms are the exact halves of the even terms in A051783. - Alexander Adamchuk, Mar 02 2008

a(29) > 2*10^5. - Robert Price, Aug 18 2014

			9^13 + 2 = 2541865828331 is prime, so 13 is a term.

Henri Lifchitz and Renaud Lifchitz, PRP Records.

Cf. A051783 (3^k + 2 is prime), A087885 (5^k + 2 is prime).

Do[ If[ PrimeQ[9^n + 2], Print[n]], {n, 1, 2250}] (* Robert G. Wilson v, Feb 06 2004 *)

for(i=0,700,if(isprime(9^i+2),print(i)))

More terms from mohammed bouayoun (bouyao(AT)wanadoo.fr), Feb 04 2004
Further terms from Robert G. Wilson v and Ray Chandler, Feb 06 2004
a(20) - a(22) found by Henri Lifchitz, a(23) found by Wojciech Florek. - Jason Earls, Feb 25 2008
a(24)-a(27) from A051783 by Ray Chandler, Aug 06 2011
a(28) from Robert Price, Aug 18 2014
Removal of erroneous term (97715) by Robert Price, Aug 19 2014

A087886 Numbers n such that 29^n + 2 is prime.

Original entry on oeis.org

0, 1, 3, 63, 87, 189, 239, 605, 2099, 3667, 5029, 20025, 45285, 99167

Offset: 1

Donald S. McDonald, Oct 13 2003

After 0, all terms are odd. [Bruno Berselli, Oct 02 2014]

			a(1) = 1 is a member because 29^1 + 2 = 31 is prime.
29^3+2 = 24391 is prime, so 3 is in the sequence.

Henri & Renaud Lifchitz, PRP Records.

Cf. A051783, n such that 3^n +2 is prime.

Cf. A087885, 5^n +2 is prime.

for( n = 0,239, if( isprime( 29^n +2), print( n), ))

a(8) from Mark Hudson (mrmarkhudson(AT)hotmail.com), Sep 07 2004
a(9) - a(11), corresponding to probable primes, from Ryan Propper, Jul 03 2005
Edited by T. D. Noe, Oct 30 2008
a(12) from Ray Chandler, Aug 01 2011
a(13) from Ray Chandler, Aug 02 2011
a(14) from Ray Chandler, Aug 08 2011

A247957 Numbers k such that 33^k + 2 is prime.

Original entry on oeis.org

0, 2, 26, 60, 218, 248, 399, 1175, 1244, 2670, 9300, 45216, 144412

Offset: 1

Vincenzo Librandi, Sep 28 2014

Some terms correspond to probable primes. Lifchitz link shows that Ray Chandler discovered 9300, and Lelio R Paula found that 45216 is in the sequence. - Jens Kruse Andersen, Sep 29 2014
Terms in the similar sequence, 53^k+2, begin with 0, 7, 14483 with the next term > 2*10^5. - Robert Price, Mar 28 2015
Confirmed that 45216 is a(12). - Robert Price, Apr 14 2015
a(14) > 2*10^5. - Robert Price, Apr 14 2015

Henri & Renaud Lifchitz, PRP Records, search for 33^n+2

Cf. numbers n such that k^n+2 is prime: A051783 (k=3), A087885 (k=5), A090649 (k=9), A109076 (k=11), A138048 (k=15), A113480 (k=17), A138049 (k=21), A138050 (k=23), A138051 (k=27), A087886 (k=29), this sequence (k=33), A247958 (k=35), A247959 (k=39), A247960 (k=41), A247961 (k=45); (0, 113) for k=47; A247962 (k=51); A247963 (k=57), A113481 (k=59).

[n: n in [0..350]| IsPrime( 33^n + 2 )];

A247957:=n->`if`(isprime(33^n+2),n,NULL): seq(A247957(n), n=0..1000); # Wesley Ivan Hurt, Sep 28 2014

Select[Range[0,1000], PrimeQ[33^# + 2] &]

is(n)=ispseudoprime(33^n+2) \\ Charles R Greathouse IV, Feb 17 2017

a(8)-a(11) from Jens Kruse Andersen, Sep 29 2014

a(12)-a(13) from Robert Price, Apr 14 2015

A138048 Numbers k such that 15^k + 2 is prime.

Original entry on oeis.org

0, 1, 2, 4, 5, 10, 11, 16, 20, 52, 75, 106, 112, 132, 371, 3264, 3424, 5477, 7516, 10365, 44557, 150706

Offset: 1

Alexander Adamchuk, Mar 02 2008

No further terms < 100000. - Ray Chandler, Aug 05 2011

a(23) > 2*10^5. - Robert Price, Jun 23 2015

Henri & Renaud Lifchitz, PRP Records.

Cf. A051783 (k such that 3^k + 2 is prime).
Cf. A087885 (k such that 5^k + 2 is prime).
Cf. A090649, A109076, A113480, A138049, A138050, A138051, A087886, A113481.

Do[ f = 15^n + 2; If[ PrimeQ[ f ], Print[ {n, f} ] ], {n, 1, 371} ]

is(n)=ispseudoprime(15^n+2) \\ Charles R Greathouse IV, Feb 17 2017

a(16)-a(19) from Ray Chandler, Jul 30 2011
a(20) found by Lelio R Paula, Dec 2006
a(21) from Ray Chandler, Jul 31 2011
a(22) from Robert Price, Jun 23 2015

A138049 Numbers k such that 21^k + 2 is prime.

Original entry on oeis.org

0, 1, 2, 4, 7, 24, 40, 112, 310, 1026, 1286, 36566, 43717, 53753

Offset: 1

Alexander Adamchuk, Mar 02 2008

No further terms < 100000. - Ray Chandler, Aug 11 2011

a(15) > 2*10^5. - Robert Price, Jul 14 2015

Henri & Renaud Lifchitz, PRP Records.

Cf. A051783 (k such that 3^k + 2 is prime).
Cf. A087885 (k such that 5^k + 2 is prime).
Cf. A090649, A109076, A113480, A138048, A138050, A138051, A087886, A113481.

Do[ f = 21^n + 2; If[ PrimeQ[ f ], Print[ {n, f} ] ], {n, 1, 310} ]

is(n)=ispseudoprime(21^n+2) \\ Charles R Greathouse IV, Feb 17 2017

from Herman Jamke (hermanjamke(AT)fastmail.fm), May 01 2008
and 36566 from Ray Chandler, Jul 31 2011
from Ray Chandler, Aug 01 2011
from Ray Chandler, Aug 02 2011

A138050 Numbers k such that 23^k + 2 is prime.

Original entry on oeis.org

0, 11, 39, 323, 12415, 14655, 27679

Offset: 1

Alexander Adamchuk, Mar 02 2008

No further terms < 100000. - Ray Chandler, Aug 03 2011

Henri & Renaud Lifchitz, PRP Records.

Cf. A051783 (k such that 3^k + 2 is prime).
Cf. A087885 (k such that 5^k + 2 is prime).
Cf. A090649, A109076, A113480, A138048, A138049, A138051, A087886, A113481.

Do[ f = 23^n + 2; If[ PrimeQ[ f ], Print[ {n, f} ] ], {n, 1, 323} ]

is(n)=ispseudoprime(23^n+2) \\ Charles R Greathouse IV, Feb 17 2017

a(5)-a(7) from Ray Chandler, Aug 01 2011

A138051 Numbers k such that 27^k + 2 is prime.

Original entry on oeis.org

0, 1, 5, 8, 12, 21, 41, 42, 81, 105, 121, 377, 501, 2401, 14597, 35381, 59476, 120536

Offset: 1

Alexander Adamchuk, Mar 02 2008

All terms are the exact thirds of terms of A051783 that are divisible by 3.

Henri & Renaud Lifchitz, PRP Records.

Cf. A051783 (3^k + 2 is prime), A087885 (5^k + 2 is prime).
Cf. A090649, A109076, A113480, A138048, A138049, A138050, A087886, A113481.
Cf. A176495.

Do[ f = 27^n + 2; If[ PrimeQ[ f ], Print[ {n, f} ] ], {n, 1, 2500} ]

is(n)=ispseudoprime(27^n+2) \\ Charles R Greathouse IV, Feb 17 2017

a(15)-a(17) from A051783 by Ray Chandler, Aug 06 2011

a(18) from Robert Price, May 12 2019

A134916 Numbers n such that both 3^n+2 and 2^n+3 are primes.

Original entry on oeis.org

1, 2, 3, 4, 15

Offset: 1

Zak Seidov, Jan 29 2008

Intersection of A057732 and A051783. a(6)>1000.

Since this is the intersection of A057732 and A051783, a(6)>95504. - Dmitry Kamenetsky, Jul 29 2008

Cf. A051783, A057732.

Select[Range[20],AllTrue[{3^#+2,2^#+3},PrimeQ]&] (* Harvey P. Dale, Sep 02 2022 *)

for(n=0,1000,if(isprime(2^n+3)&&isprime(3^n+2),print(n)))

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A219051 Numbers k such that 3^k - 34 is prime.

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A087885 Numbers k such that 5^k + 2 is a prime.

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A090649 Numbers k such that 9^k + 2 is prime.

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A087886 Numbers n such that 29^n + 2 is prime.

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A247957 Numbers k such that 33^k + 2 is prime.

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A138048 Numbers k such that 15^k + 2 is prime.

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A138049 Numbers k such that 21^k + 2 is prime.

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