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A363072 Add primes until a perfect power appears. When a perfect power appears, that term is the smallest root of the perfect power. Then return to adding primes, beginning with the next prime.

%I A363072 #9 Jun 23 2023 17:04:35
%S A363072 2,5,10,17,28,41,58,77,10,39,70,107,148,191,238,291,350,411,478,549,
%T A363072 622,701,28,117,214,315,418,525,634,747,874,1005,1142,1281,1430,1581,
%U A363072 1738,1901,2068,2241,2420,51,242,435,632,831,1042,1265,1492,1721,1954,2193
%N A363072 Add primes until a perfect power appears. When a perfect power appears, that term is the smallest root of the perfect power. Then return to adding primes, beginning with the next prime.
%e A363072 The first term is the first prime, p(1) = 2
%e A363072 a(1) = p(1) = 2
%e A363072 a(2) = a(1) + p(2) = 2 + 3 = 5
%e A363072 a(3) = a(2) + p(3) = 5 + 5 = 10
%e A363072 etc.
%e A363072 a(8) = 58 + 19 = 77
%e A363072 a(9) is determined:
%e A363072 a(8) + p(9) = 77 + 23 = 100, a perfect power.  10 is the smallest root of 100, therefore a(9) = 10
%e A363072 a(10) = 10 + p(10) = 10 + 29 = 39
%e A363072 and so on.
%t A363072 root[n_] := Surd[n, GCD @@ FactorInteger[n][[;; , 2]]]; a[1] = 2; a[n_] := a[n] = root[a[n - 1] + Prime[n]]; Array[a, 100] (* _Amiram Eldar_, May 21 2023 *)
%Y A363072 Cf. A001597.
%K A363072 nonn,easy
%O A363072 1,1
%A A363072 _Damon Lay_, May 16 2023