|
| |
|
|
A121620
|
|
Smallest prime of the form k^p - (k-1)^p, where p = prime(n).
|
|
8
|
|
|
|
3, 7, 31, 127, 313968931, 8191, 131071, 524287, 777809294098524691, 68629840493971, 2147483647, 114867606414015793728780533209145917205659365404867510184121, 44487435359130133495783012898708551, 1136791005963704961126617632861
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
All Mersenne primes of form 2^p-1 = {3, 7, 31, 127, 8191,...} belong to a(n). Mersenne prime A000668(n) = a(k) when prime(k) = A000043(n). Last digit is always 1 for Nexus numbers of form n^p - (n-1)^p with p = {5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101,...} = A004144(n) Pythagorean primes: primes of form 4n+1.
|
|
|
LINKS
|
Vladimir Pletser and T. D. Noe, Table of n, a(n) for n = 1..80 (first 46 terms from Vladimir Pletser)
|
|
|
MATHEMATICA
|
t = {}; n = 0; While[n++; p = Prime[n]; k = 1; While[q = (k + 1)^p - k^p; ! PrimeQ[q], k++]; q < 10^100, AppendTo[t, q]]; t (* T. D. Noe, Feb 12 2013 *)
|
|
|
CROSSREFS
|
Cf. A121616, A121617, A121618, A121619, A022521, A022523, A004144, A000043, A000668.
Sequence in context: A136007 A084732 A123488 * A042271 A000644 A015459
Adjacent sequences: A121617 A121618 A121619 * A121621 A121622 A121623
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Alexander Adamchuk, Aug 10 2006
|
|
|
STATUS
|
approved
|
| |
|
|
