A085418 Primes reached in A085417.
3, 5, 17, 11, 29, 19, 41, 127, 53, 89, 67, 107, 83, 277, 113, 233, 113, 79, 127, 157, 139, 101, 181, 113, 293, 127, 313, 257, 199, 239, 223, 163, 239, 173, 257, 467, 271, 541, 461, 383, 349, 223, 563, 787, 383, 389, 1021, 271, 647, 1489, 389, 509, 1789, 773, 983
Offset: 1
Examples
a(3)=17 because prime[3]=5 and 5+(3+4+5)=17 is a prime.