A058958 -id:A058958 - cp's OEIS frontend

A102903 Primes of the form 3^k + 4.

5, 7, 13, 31, 733, 19687, 59053, 31381059613, 205891132094653, 109418989131512359213, 1570042899082081611640534567, 323257909929174534292273980721360271853391

Offset: 1

Roger L. Bagula, Mar 01 2005

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..17

Cf. A000040, A058958 (associated k).

Cf. Primes of the form 3^k + d: A057735 (d=2), this sequence (d=4), A102870 (d=8), A102907 (d=10), A102874 (d=14), A243437 (d=16), A102904 (d=20), A243438 (d=22), A243439 (d=26), A102906 (d=28).

[a: n in [0..100] | IsPrime(a) where a is 3^n+4]; // Vincenzo Librandi, Jul 19 2012

Select[Table[3^n+4,{n,0,200}],PrimeQ] (* Vincenzo Librandi, Jul 19 2012 *)

a(n) = 3^A058958(n) + 4. - Elmo R. Oliveira, Nov 09 2023

Edited by Zak Seidov, Aug 29 2014

A217384 Numbers k such that 9^k + 4 is prime.

Original entry on oeis.org

0, 1, 3, 5, 11, 15, 21, 87, 99, 281, 497, 2919, 6849, 7365, 8483, 49317, 58611

Offset: 1

Vincenzo Librandi, Oct 04 2012

Contribution from Bruno Berselli, Oct 04 2012: (Start)
Contains exactly the halved even terms of A058958.
Naturally, apart from the first term, these numbers are odd since (10-1)^(2n)+4 is divisible by 5. (End)
a(18) > 10^5. - Tyler NeSmith, May 05 2021

Cf. A058958, A090649.

Select[Range[0, 3000], PrimeQ[9^# + 4] &]

is(n)=ispseudoprime(9^n+4) \\ Charles R Greathouse IV, Feb 20 2017

a(13)-a(14) from Bruno Berselli, Oct 04 2012

a(15)-a(17) from Tyler NeSmith, May 05 2021

A243397 Numbers n such that 19^n+4 is prime.

Original entry on oeis.org

0, 1, 3, 21, 145, 273, 1425, 9613, 15711, 18445

Offset: 1

Felix Fröhlich, Jun 04 2014

No further terms up to 20000. - Felix Fröhlich, Oct 29 2014
No further terms up to 24000. - Felix Fröhlich, Jan 22 2015
No further terms up to 50000. - Michael S. Branicky, Oct 09 2024

Corresponding sequences for k^n+4: A058958 (k=3), A124621 (k=5), A096305 (k=7), A217384 (k=9), A137236 (k=13).

[n: n in [0..1000] | IsPrime(19^n+4)]; // Vincenzo Librandi, Oct 16 2014

Select[Range[0, 10000], PrimeQ[19^# + 4] &] (* Vincenzo Librandi, Oct 16 2014 *)

for(n=0, 10^5, if(ispseudoprime(19^n+4), print1(n, ", ")))

a(1)-a(2) prepended by N. J. A. Sloane, Jun 18 2014

a(9)-a(10) from Felix Fröhlich, Oct 16 2014

A247166 Numbers k such that 15^k+4 is prime.

Original entry on oeis.org

0, 1, 2, 7, 10, 39, 42, 201, 225, 551

Offset: 1

Felix Fröhlich, Dec 01 2014

No further terms up to 10000.

No further terms up to 10^5. - Tyler NeSmith, Jan 21 2021

Corresponding sequences for m^k+4: A058958 (m=3), A124621 (m=5), A096305 (m=7), A217384 (m=9), A137236 (m=13), A243397 (m=19).

[n: n in [0..300] | IsPrime(15^n+4)]; // Vincenzo Librandi, Dec 01 2015

a247166[n_Integer] := Select[Range[n], PrimeQ[15^# + 4] &]; a247166[10^4] (* Michael De Vlieger, Dec 03 2014 *)

for(n=0, 1e5, if(ispseudoprime(15^n+4), print1(n, ", ")))

Offset changed to 1 by Georg Fischer, Sep 26 2022

A230433 Numbers k such that 43^k + 4 is prime.

Original entry on oeis.org

1, 7, 13, 17, 33, 43, 205, 287, 669, 1161, 1166, 3753, 6095, 18123, 28041

Offset: 1

Robert Price, Oct 18 2013

a(16) > 5*10^4.

Cf. A058958.

Do[If[PrimeQ[43^k + 4], Print[k]], {k, 50000}]

A305531 Smallest k >= 1 such that (n-1)*n^k + 1 is prime.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 2, 1, 3, 10, 3, 1, 2, 1, 1, 4, 1, 29, 14, 1, 1, 14, 2, 1, 2, 4, 1, 2, 4, 5, 12, 2, 1, 2, 2, 9, 16, 1, 2, 80, 1, 2, 4, 2, 3, 16, 2, 2, 2, 1, 15, 960, 15, 1, 4, 3, 1, 14, 1, 6, 20, 1, 3, 946, 6, 1, 18, 10, 1, 4, 1, 5, 42, 4, 1, 828, 1, 1, 2, 1, 12, 2, 6, 4, 30, 3, 3022, 2, 1, 1

Offset: 2

Eric Chen, Jun 04 2018

nonn

a(prime(j)) + 1 = A087139(j).
a(123) > 10^5, a(342) > 10^5, see the Barnes link for the Sierpinski base-123 and base-342 problems.
a(251) > 73000, see A087139.

Eric Chen, Table of n, a(n) for n = 2..122
Gary Barnes, Sierpinski conjectures and proofs
Eric Chen, Table n, a(n) for n = 2..360 status

For the numbers k such that these forms are prime:
a1(b): numbers k such that (b-1)*b^k-1 is prime
a2(b): numbers k such that (b-1)*b^k+1 is prime
a3(b): numbers k such that (b+1)*b^k-1 is prime
a4(b): numbers k such that (b+1)*b^k+1 is prime (no such k exists when b == 1 (mod 3))
a5(b): numbers k such that b^k-(b-1) is prime
a6(b): numbers k such that b^k+(b-1) is prime
a7(b): numbers k such that b^k-(b+1) is prime
a8(b): numbers k such that b^k+(b+1) is prime (no such k exists when b == 1 (mod 3)).
Using "-------" if there is currently no OEIS sequence and "xxxxxxx" if no such k exists (this occurs only for a4(b) and a8(b) for b == 1 (mod 3)):
.
   b   a1(b)   a2(b)   a3(b)   a4(b)   a5(b)   a6(b)   a7(b)   a8(b)
--------------------------------------------------------------------
   2 A000043 ------- A002235 A002253 A000043 ------- A050414 A057732
   3 A003307 A003306 A005540 A005537 A014224 A051783 A058959 A058958
   4 A272057 ------- ------- xxxxxxx A059266 A089437 A217348 xxxxxxx
   5 A046865 A204322 A257790 A143279 A059613 A124621 A165701 A089142
   6 A079906 A247260 ------- ------- A059614 A145106 A217352 A217351
   7 A046866 A245241 ------- xxxxxxx A191469 A217130 A217131 xxxxxxx
   8 A268061 A269544 ------- ------- A217380 A217381 A217383 A217382
   9 A268356 A056799 ------- ------- A177093 A217385 A217493 A217492
  10 A056725 A056797 A111391 xxxxxxx A095714 A088275 A092767 xxxxxxx
  11 A046867 A057462 ------- ------- ------- ------- ------- -------
  12 A079907 A251259 ------- ------- ------- A137654 ------- -------
  13 A297348 ------- ------- xxxxxxx ------- ------- ------- xxxxxxx
  14 A273523 ------- ------- ------- ------- ------- ------- -------
  15 ------- ------- ------- ------- ------- ------- ------- -------
  16 ------- ------- ------- xxxxxxx ------- ------- ------- xxxxxxx
Cf. (smallest k such that these forms are prime) A122396 (a1(b)+1 for prime b), A087139 (a2(b)+1 for prime b), A113516 (a5(b)), A076845 (a6(b)), A178250 (a7(b)).

a(n)=for(k=1,2^16,if(ispseudoprime((n-1)*n^k+1),return(k)))

A253380 Numbers k such that 17^k + 4 is prime.

Original entry on oeis.org

0, 2, 6, 18, 7238

Offset: 1

Felix Fröhlich, Dec 31 2014

No further terms up to 10000.

No further terms up to 37200. - Michael S. Branicky, Mar 22 2023

			For k = 0: 17^0 + 4 = 5, which is prime, so 0 is a term of the sequence.
For k = 2: 17^2 + 4 = 293, which is prime, so 2 is a term of the sequence.

Corresponding sequences for k^n+4: A058958 (k=3), A124621 (k=5), A096305(k=7), A217384 (k=9), A137236 (k=13), A247166 (k=15), A243397 (k=19).

Select[Range@10^5, PrimeQ[17^# + 4] &] (* Michael De Vlieger, Jan 03 2015 *)

for(n=0, 1e5, if(ispseudoprime(17^n+4), print1(n, ", ")))

cp's OEIS Frontend

A102903 Primes of the form 3^k + 4.

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A217384 Numbers k such that 9^k + 4 is prime.

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A243397 Numbers n such that 19^n+4 is prime.

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A247166 Numbers k such that 15^k+4 is prime.

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Magma

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A230433 Numbers k such that 43^k + 4 is prime.

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Mathematica

A305531 Smallest k >= 1 such that (n-1)*n^k + 1 is prime.

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PARI

A253380 Numbers k such that 17^k + 4 is prime.

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Programs

Mathematica

PARI