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%I #20 Apr 01 2024 11:30:17
%S 3,7,31,127,313968931,8191,131071,524287,777809294098524691,
%T 68629840493971,2147483647,
%U 114867606414015793728780533209145917205659365404867510184121,44487435359130133495783012898708551,1136791005963704961126617632861
%N Smallest prime of the form k^p - (k-1)^p, where p = prime(n).
%C 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.
%H Vladimir Pletser and T. D. Noe, <a href="/A121620/b121620.txt">Table of n, a(n) for n = 1..80</a> (first 46 terms from Vladimir Pletser)
%t 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 *)
%t 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 *)
%Y Cf. A121616, A121617, A121618, A121619, A022521, A022523, A004144, A000043, A000668.
%K nonn
%O 1,1
%A _Alexander Adamchuk_, Aug 10 2006
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