Thomas R. Nicely, <a href="https://faculty.lynchburg.edu/~nicely/gaps/gaplist.html">First occurrence prime gaps</a> [For local copy see A000101].
Thomas R. Nicely, <a href="httphttps://wwwfaculty.trnicelylynchburg.netedu/~nicely
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Smallest prime p such that the gap between p and the next prime, q, is a perfect power (as in A001597).
First occurrence of prime gaps which are perfect powers.
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Smallest prime p such that the gap between p and the next prime, q, is a perfect power (as in A001597).
The old definition is was confusing - there is only one such prime. Also, it is not meant that for each term of A001597 (perfect powers), the smallest prime followed by that gap is listed. What is meant was: primes p such that nextprime(p)-p is an element of A001597 (or A075090: even perfect powers, for n > 1), and p is the smallest prime followed by this gap. - M. F. Hasler, Oct 18 2018
Better definition from M. F. Hasler, Oct 18 2018
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NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ@k, k++ ]; k]; perfectPowerQ[x_] := GCD @@ Last /@ FactorInteger@x > 1; dd = {1}; pp = {2}; qq = {3}; p = 3; Do[q = NextPrim@p; d = q - p; If[perfectPowerQ@d && ! MemberQ[dd, d], Print@q; AppendTo[pp, p]; AppendTo[dd, d]]; p = q, {n, 10^7}]; pp (* Robert G. Wilson v , Nov 03 2006 *)
Edited and extended by Robert G. Wilson v , Nov 03 2006, and corrected Nov 04 2006
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A138198 is a subsequence. - M. F. Hasler, Oct 18 2018
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