A121620 Smallest prime of the form k^p - (k-1)^p, where p = prime(n).

3, 7, 31, 127, 313968931, 8191, 131071, 524287, 777809294098524691, 68629840493971, 2147483647, 114867606414015793728780533209145917205659365404867510184121, 44487435359130133495783012898708551, 1136791005963704961126617632861

Offset: 1

Author

Alexander Adamchuk, Aug 10 2006

Keywords

• nonn

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)

Crossrefs

Cf. A121616, A121617, A121618, A121619, A022521, A022523, A004144, A000043, A000668.

Programs

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 *)
spf[p_]:=Module[{k=2},While[CompositeQ[k^p-(k-1)^p],k++];k^p-(k-1)^p]; Table[spf[p],{p,Prime[ Range[20]]}] (* Harvey P. Dale, Apr 01 2024 *)