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

1,1

Links

Table of n, a(n) for n=1..52.

Example

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.

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 *)

Crossrefs

Cf. A001597.

Sequence in context: A246883 A329864 A174910 * A301273 A007504 A172059

Adjacent sequences: A363069 A363070 A363071 * A363073 A363074 A363075

Keyword

nonn,easy

Author

Damon Lay, May 16 2023

Status

approved