A133266 a(1) = 30; for n >= 2, choose smallest a(n) so that no sum of 2 or more terms equals a prime.
30, 32, 33, 52, 60, 63, 90, 120, 150, 180, 210, 240, 270, 300, 330, 360, 390, 420, 450, 480, 510, 540, 570, 600, 630, 660, 690, 720, 750, 780
Offset: 1
Programs
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Mathematica
(* first do *) Needs [ "Combinatorica`" ] (* then *) lst = {30}; g [ k_ ] := Block [ {j = 1, l = 2^Length@ lst}, While [ j < l && !PrimeQ [ Plus @@ NthSubset [ j, lst ] + k ], j++ ]; If [ j == l, False, True ] ]; f [ n_ ] := Block [ {k = lst [ [ -1 ] ] + 1}, While [ g@k == True, k++ ]; AppendTo [ lst, k ]; k ]; Do [ Print@ f@n, {n, 30} ]
Formula
a(n+1) = a(n) + 30 for n >= 7 (conjectured). - Chai Wah Wu, Feb 15 2020