A082387 -id:A082387 - cp's OEIS frontend

A128345 Numbers k such that (8^k - 5^k)/3 is prime.

2, 19, 1021, 5077, 34031, 46099, 65707, 347437

Offset: 1

Alexander Adamchuk, Feb 27 2007

All terms are primes.
No further terms up to 5000 - Harvey P. Dale, Mar 23 2011
a(8) > 10^5 - Robert Price, Dec 22 2012
a(9) > 10^6 - Jon Grantham, Jul 29 2023

Jon Grantham and Andrew Granville, Fibonacci primes, primes of the form 2^n-k and beyond, arXiv:2307.07894 [math.NT], 2023.

Cf. A062572, A128344, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.
Cf. A004061, A082182, A121877, A059802.
Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128341, A128342.

k=8; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n,1,200}]
Select[Range[5000],PrimeQ[(8^#-5^#)/3]&]  (* Harvey P. Dale, Mar 23 2011 *)

is(n)=isprime((8^n-5^n)/3) \\ Charles R Greathouse IV, Feb 17 2017

a(4)-a(7) from Robert Price, Dec 22 2012

a(8) from Jon Grantham, Jul 29 2023

A128352 Numbers k such that (17^k - 5^k)/12 is prime.

Original entry on oeis.org

5, 7, 17, 23, 43, 71, 239, 733, 1097

Offset: 1

Alexander Adamchuk, Feb 27 2007

All terms are primes.

a(10) > 10^5. - Robert Price, Jun 11 2013

Cf. A062572, A128344, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128353, A128354.
Cf. A004061, A082182, A121877, A059802.
Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128341, A128342.

k=17; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n,1,100}]

is(n)=isprime((17^n-5^n)/12) \\ Charles R Greathouse IV, Feb 17 2017

A128353 Numbers k such that (18^k - 5^k)/13 is prime.

Original entry on oeis.org

2, 3, 19, 23, 31, 37, 251, 283, 977, 28687, 32993

Offset: 1

Alexander Adamchuk, Feb 27 2007

All terms are primes.

a(12) > 10^5. - Robert Price, Aug 10 2013

Cf. A062572, A128344, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128354.
Cf. A004061, A082182, A121877, A059802.
Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128341, A128342.

k=18; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n,1,100}]

is(n)=isprime((18^n-5^n)/13) \\ Charles R Greathouse IV, Feb 17 2017

a(10)-a(11) from Robert Price, Aug 10 2013

A128354 Numbers k such that (19^k - 5^k)/14 is prime.

Original entry on oeis.org

5, 17, 31, 59, 373, 643, 2843, 5209, 85009

Offset: 1

Alexander Adamchuk, Feb 27 2007

All terms are primes.

a(10) > 10^5. - Robert Price, Jul 22 2013

Cf. A062572, A128344, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353.
Cf. A004061, A082182, A121877, A059802.
Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128341, A128342.

k=19; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n,1,100}]

is(n)=isprime((19^n-5^n)/14) \\ Charles R Greathouse IV, Feb 17 2017

a(7)-a(9) from Robert Price, Jul 22 2013

A128349 Numbers k such that (13^k - 5^k)/8 is prime.

Original entry on oeis.org

5, 19, 71, 197, 659, 22079, 61949

Offset: 1

Alexander Adamchuk, Feb 27 2007

All terms are primes.

a(8) > 10^5. - Robert Price, Mar 05 2013

Cf. A062572, A128344, A128345, A128346, A128347, A128348, A128350, A128351, A128352, A128353, A128354.
Cf. A004061, A082182, A121877, A059802.
Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128341, A128342.

k=13; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n,1,100}]

is(n)=isprime((13^n-5^n)/8) \\ Charles R Greathouse IV, Feb 17 2017

a(6)-a(7) from Robert Price, Mar 05 2013

A128350 Numbers k such that (14^k - 5^k)/9 is prime.

Original entry on oeis.org

2, 151, 673, 709, 2999, 17909, 77213

Offset: 1

Alexander Adamchuk, Feb 27 2007

All terms are primes.

a(8) > 10^5. - Robert Price, Apr 23 2013

Cf. A062572, A128344, A128345, A128346, A128347, A128348, A128349, A128351, A128352, A128353, A128354. Cf. A004061, A082182, A121877, A059802. Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128341, A128342.

k=14; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n,1,200}]

is(n)=isprime((14^n-5^n)/9) \\ Charles R Greathouse IV, Feb 17 2017

One more term from Herman Jamke (hermanjamke(AT)fastmail.fm), May 01 2008

a(6) and a(7) from Robert Price, Apr 23 2013

A128351 Numbers k such that (16^k - 5^k)/11 is prime.

Original entry on oeis.org

7, 13, 109, 139, 967, 60013, 97613

Offset: 1

Alexander Adamchuk, Feb 27 2007

All terms are primes.

a(8) > 10^5. - Robert Price, Jul 03 2013

Cf. A062572, A128344, A128345, A128346, A128347, A128348, A128349, A128350, A128352, A128353, A128354, A004061, A082182, A121877, A059802, A057171, A082387, A122853, A128335-A128342.

k=16; Do[p=Prime[n]; f=(k^p-5^p)/(k-5); If[ PrimeQ[f], Print[p] ], {n,1,100}]

is(n)=isprime((16^n-5^n)/11) \\ Charles R Greathouse IV, Feb 17 2017

a(6)-a(7) from Robert Price, Jul 03 2013

A128338 Numbers k such that (8^k + 5^k)/13 is prime.

Original entry on oeis.org

7, 19, 167, 173, 223, 281, 21647

Offset: 1

Alexander Adamchuk, Feb 27 2007

All terms are primes.

a(8) > 10^5. - Robert Price, Jan 21 2013

Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128339, A128340, A128341, A128342, A128343. Cf. A004061, A082182, A121877, A059802. Cf. A062572, A128344, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.

k=8; Do[p=Prime[n]; f=(k^p+5^p)/(k+5); If[ PrimeQ[f], Print[p] ], {n,1,100}]

is(n)=isprime((8^n+5^n)/13) \\ Charles R Greathouse IV, Feb 17 2017

a(7) from Robert Price, Jan 21 2013

A128343 Numbers k such that (14^k + 5^k)/19 is prime.

Original entry on oeis.org

3, 7, 17, 79, 17477, 19319, 49549

Offset: 1

Alexander Adamchuk, Feb 27 2007

All terms are primes.

a(8) > 10^5. - Robert Price, May 20 2013

Cf. A057171, A082387, A122853, A128335, A128336, A128337, A128338, A128339, A128340, A128341, A128342.
Cf. A004061, A082182, A121877, A059802.
Cf. A062572, A128344, A128345, A128346, A128347, A128348, A128349, A128350, A128351, A128352, A128353, A128354.

k=14; Do[p=Prime[n]; f=(k^p+5^p)/(k+5); If[ PrimeQ[f], Print[p] ], {n,1,100}]

is(n)=isprime((14^n+5^n)/19) \\ Charles R Greathouse IV, Feb 17 2017

a(5)-a(7) from Robert Price, May 20 2013

A125956 Numbers k such that (2^k + 9^k)/11 is prime.

Original entry on oeis.org

3, 7, 127, 283, 883, 1523, 4001

Offset: 1

Alexander Adamchuk, Feb 06 2007

All terms are primes. Note that first 3 terms {3, 7, 127} are primes of the form 2^q - 1, where q = {2, 3, 7} is prime too. Corresponding primes of the form (2^k + 9^k)/11 are {67, 434827, ...}.

a(8) > 10^5. - Robert Price, Dec 23 2012

Cf. A000978 = numbers n such that (2^n + 1)/3 is prime.
Cf. A057469 = numbers n such that (2^n + 3^n)/5 is prime.
Cf. A082387 = numbers n such that (2^n + 5^n)/7 is prime.

Do[p=Prime[n];f=(2^p+9^p)/11; If[PrimeQ[f], Print[{p, f}]], {n, 1, 100}]

is(n)=ispseudoprime((2^n+9^n)/11) \\ Charles R Greathouse IV, Feb 20 2017

2 more terms from Rick L. Shepherd, Feb 14 2007

a(7) from Robert Price, Dec 23 2012

cp's OEIS Frontend

A128345 Numbers k such that (8^k - 5^k)/3 is prime.

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A128352 Numbers k such that (17^k - 5^k)/12 is prime.

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A128353 Numbers k such that (18^k - 5^k)/13 is prime.

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A128354 Numbers k such that (19^k - 5^k)/14 is prime.

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A128349 Numbers k such that (13^k - 5^k)/8 is prime.

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A128350 Numbers k such that (14^k - 5^k)/9 is prime.

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A128351 Numbers k such that (16^k - 5^k)/11 is prime.

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A128338 Numbers k such that (8^k + 5^k)/13 is prime.

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