A081505 -id:A081505 - cp's OEIS frontend

A219283 Primes of the form 13^k - 12^k.

6431804812640900941, 31211427601852046808999765129652549, 4519079836942618423019040742735616921552429101, 22137406298265966315641393147750228275603823278911109

Offset: 1

Vincenzo Librandi, Nov 23 2012

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..7

Cf. A058765, A147667, A147669, A199820, A082101, A081505.

Cf. A062579 (associated k).

[a: n in [0..200] | IsPrime(a) where a is  13^n - 12^n];

Select[Table[13^n - 12^n, {n, 0, 200}], PrimeQ]

A286348 Numbers n such that 4^n + (-3)^n is prime.

Original entry on oeis.org

0, 3, 4, 7, 16, 17, 59, 283, 311, 383, 499, 521, 541, 599, 1193, 1993, 2671, 7547, 24019, 46301, 48121, 68597, 91283, 131497, 148663, 184463, 341233

Offset: 1

Juri-Stepan Gerasimov, May 07 2017

Numbers n such that (1 + k)^n + (-k)^n is prime:
0 (k = 0);
A285929 (k = 1);
A283653 (k = 2);
this sequence (k = 3);
0, 2, 3, 4, 43, 59, 191, 223, ... (k = 4);
0, 2, 5, 8, 11, 13, 16, 23, 61, 83, ...(k = 5);
0, 3, 4, 7, 16, 29, 41, 67, ... (k = 6);
0, 2, 7, 11, 16, 17, 29, 31, 79, 43, 131, 139, ... (k = 7);
0, 4, 7, 29, 31, 32, 67, ... (k = 8);
0, 2, 3, 4, 7, 11, 19, 29, ... (k = 9);
0, 3, 5, 19, 32, ... (k = 10);
0, 3, 7, 89, 101, ... (k = 11);
0, 2, 4, 17, 31, 32, 41, 47, 109, 163, ... (k = 12);
0, 3, 4, 11, 83, ... (k = 13);
0, 2, 3, 4, 16, 43, 173, 193, ... (k = 14);
0, 43, ... (k = 15);
0, 4, 5, 7, 79, ... (k = 16);
0, 2, 3, 8, 13, 71, ... (k = 17);
0, 1607, ... (k = 18);
...
Primes of the form (1 + n)^(2^n) + n: 5, 83, 65539, 7958661109946400884391941, ...
Numbers m such that (1 + k)^m + (-k)^m is not odd prime for k =< m: 0, 1, 15, 18, 53, 59, 106, 114, 124, 132, 133, 143, 177, 214, 232, 234, 240, 256, ...
Conjecture: if (1 + y)^x + (-y)^x is a prime number then x is zero, or an even power of two, or an odd prime number.

			3 is in this sequence because 4^3 + (-3)^3 = 37 is prime.
4 is in this sequence because 4^4 + (-3)^4 = 337 is prime.

Cf. A059801, A081505, A283653, A285929.

[n: n in [0..250] | IsPrime(4^n+(-3)^n)];

Select[Range[0, 3000], PrimeQ[4^# + (-3)^#] &] (* Michael De Vlieger, May 09 2017 *)

is(n)=ispseudoprime(4^n+(-3)^n) \\ Charles R Greathouse IV, Jun 13 2017

cp's OEIS Frontend

A219283 Primes of the form 13^k - 12^k.

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