A122853 -id:A122853 - 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

A128066 Numbers k such that (3^k + 4^k)/7 is prime.

Original entry on oeis.org

3, 5, 19, 37, 173, 211, 227, 619, 977, 1237, 2437, 5741, 13463, 23929, 81223, 121271

Offset: 1

Alexander Adamchuk, Feb 14 2007

All terms are primes.

Henri Lifchitz & Renaud Lifchitz, Top probable primes of the form (4^p+3^p)/7

Cf. A007658 = n such that (3^n + 1)/4 is prime; A057469 ((3^n + 2^n)/5); A122853 ((3^n + 5^n)/8).
Cf. A128067, A128068, A128069, A128070, A128071, A128072, A128073, A128074, A128075.
Cf. A059801 (4^n - 3^n); A121877 ((5^n - 3^n)/2).
Cf. A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.

a:=proc(n) if type((3^n+4^n)/7,integer)=true and isprime((3^n+4^n)/7)=true then n else fi end: seq(a(n),n=1..1500); # Emeric Deutsch, Feb 17 2007

Do[ p=Prime[n]; f=(3^p+4^p)/(4+3); If[ PrimeQ[f], Print[p]], {n,1,100} ]

f(n)=(3^n + 4^n)/7;
forprime(n=3,10^5,if(ispseudoprime(f(n)),print1(n,", ")))
/* Joerg Arndt, Mar 27 2011 */

3 more terms from Emeric Deutsch, Feb 17 2007
2 more terms from Farideh Firoozbakht, Apr 16 2007
Two more terms (13463 and 23929) found by Lelio R Paula in 2008 corresponding to probable primes with 8105 and 14406 digits. Jean-Louis Charton, Oct 06 2010
Two more terms (81223 and 121271) found by Jean-Louis Charton in March 2011 corresponding to probable primes with 48901 and 73012 digits

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

A128071 Numbers k such that (3^k + 13^k)/16 is prime.

Original entry on oeis.org

3, 7, 127, 2467, 3121, 34313

Offset: 1

Alexander Adamchuk, Feb 14 2007

All terms are primes.
a(4) is certified prime by primo; a(5) is a probable prime. - Ray G. Opao, Aug 02 2007
a(7) > 10^5. - Robert Price, Apr 14 2013

Cf. A007658 = numbers n such that (3^n + 1)/4 is prime. Cf. A057469 = numbers n such that (3^n + 2^n)/5 is prime. Cf. A122853 = numbers n such that (3^n + 5^n)/8 is prime. Cf. A128066, A128067, A128068, A128069, A128070, A128072, A128073, A128074, A128075. Cf. A059801 = numbers n such that 4^n - 3^n is prime. Cf. A121877 = numbers n such that (5^n - 3^n)/2 is a prime. Cf. A128024, A128025, A128026, A128027, A128028, A128029, A128030, A128031, A128032.

k=13; Do[ p=Prime[n]; f=(3^p+k^p)/(k+3); If[ PrimeQ[f], Print[p]], {n,1,100} ]

is(n)=isprime((3^n+13^n)/16) \\ Charles R Greathouse IV, Feb 17 2017

One more term from Ray G. Opao, Aug 02 2007

a(6) from Robert Price, Apr 14 2013

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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A128066 Numbers k such that (3^k + 4^k)/7 is prime.

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