Nondecreasing sequence of numbers whose squares (after the first term) sum to primes.
1, 1, 1, 2, 2, 6, 6, 12, 36, 36, 42, 54, 102, 102, 102, 144, 162, 216, 240, 240, 240, 252, 300, 420, 456, 510, 522, 534, 534, 558, 600, 624, 624, 642, 642, 648, 714, 738, 750, 774, 816, 888, 894, 900, 954, 978, 996, 1038, 1050, 1074, 1098, 1110, 1116, 1152
1
Sequence S000821 lists the primes formed. The linear case is handled in A075569 and A070866.
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]; t1
Cf. A075569, A070866, S000821.
nonn
T. D. Noe, Dec 29 2015