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%I #12 Feb 17 2018 18:34:21
%S 1,1,1,2,2,4,6,6,6,8,10,12,12,12,14,16,18,18,18,24,32,34,36,38,42,46,
%T 48,54,56,64,68,78,90,90,94,102,114,122,124,134,144,148,150,152,160,
%U 168,170,178,182,190,192,200,216,220,222,234,234,234,246,260,264,268,270
%N a(1)=1, then smallest number >= the previous term such that every partial sum is a prime.
%t a[1] = 1; a[n_] := a[n] = For[an = a[n-1], True, an++, If[AllTrue[ac = Rest @ Accumulate[Append[Array[a, n-1], an]], PrimeQ], Return[an]]]; Array[a, 100] (* _Jean-François Alcover_, Feb 17 2018 *)
%K nonn
%O 1,4
%A _Amarnath Murthy_, Sep 25 2002
%E More terms from _David Wasserman_, Jan 20 2005