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A121620
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Smallest prime of the form k^p - (k-1)^p, where p = prime(n).
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8
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3, 7, 31, 127, 313968931, 8191, 131071, 524287, 777809294098524691, 68629840493971, 2147483647, 114867606414015793728780533209145917205659365404867510184121, 44487435359130133495783012898708551, 1136791005963704961126617632861
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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