Primes formed by sequence S000820.
2, 3, 7, 11, 47, 83, 227, 1523, 2819, 4583, 7499, 17903, 28307, 38711, 59447, 85691, 132347, 189947, 247547, 305147, 368651, 458651, 635051, 842987, 1103087, 1375571, 1660727, 1945883, 2257247, 2617247, 3006623, 3395999, 3808163, 4220327, 4640231
1
These numbers appear to grow bi-quadratically.
T. D. Noe, Plot of 1000 terms
T. D. Noe, Table of 1000 terms
(Mma) sum = 1; k = 1; s = {{1, 0}}; Do[While[! PrimeQ[p = sum + k^2], k++]; AppendTo[s, {k, p}]; sum = p, {50}]; {t1, t2} = Transpose[s]; Rest[t2]
Cf. S000820.
nonn
T. D. Noe, Dec 29 2015