A362138 a(n) = gpf(a(n-1) + prime(n)) where gpf is the greatest prime factor and a(1)=2.

2, 5, 5, 3, 7, 5, 11, 5, 7, 3, 17, 3, 11, 3, 5, 29, 11, 3, 7, 13, 43, 61, 3, 23, 5, 53, 13, 5, 19, 11, 23, 11, 37, 11, 5, 13, 17, 5, 43, 3, 13, 97, 3, 7, 17, 3, 107, 11, 17, 41, 137, 47, 3, 127, 3, 19, 3, 137, 23, 19, 151, 37, 43, 59, 31, 29, 5, 19, 61, 41, 197

Offset: 1

Author

Sebastian F. Orellana, Jun 12 2023

Keywords

• nonn

Examples

			a(3) = gpf(a(2) + prime(3)) = gpf(5+5) = 5.
		

Links

• Sebastian F. Orellana, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006530 (gpf), A000040.

Cf. A076560, A076561.

Programs

Mathematica

gpf[n_] := FactorInteger[n][[-1, 1]]; a[1] = 2; a[n_] := a[n] = gpf[a[n - 1] + Prime[n]]; Array[a, 100] (* Amiram Eldar, Jun 15 2023 *)

Python

from sympy import factorint, prime
list=[2]
num=1
k=50
for i in range(0, k):
  list.append(max(factorint(list[i]+prime(i+1))))
print(list)