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.

2, 5, 10, 17, 28, 41, 58, 77, 10, 39, 70, 107, 148, 191, 238, 291, 350, 411, 478, 549, 622, 701, 28, 117, 214, 315, 418, 525, 634, 747, 874, 1005, 1142, 1281, 1430, 1581, 1738, 1901, 2068, 2241, 2420, 51, 242, 435, 632, 831, 1042, 1265, 1492, 1721, 1954, 2193

Offset: 1

Author

Damon Lay, May 16 2023

Keywords

• nonn
• easy

Examples

			The first term is the first prime, p(1) = 2
a(1) = p(1) = 2
a(2) = a(1) + p(2) = 2 + 3 = 5
a(3) = a(2) + p(3) = 5 + 5 = 10
etc.
a(8) = 58 + 19 = 77
a(9) is determined:
a(8) + p(9) = 77 + 23 = 100, a perfect power.  10 is the smallest root of 100, therefore a(9) = 10
a(10) = 10 + p(10) = 10 + 29 = 39
and so on.
		

Crossrefs

Cf. A001597.

Programs

Mathematica

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 *)