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%I #7 Apr 09 2013 11:38:04
%S 2,3,19,160019,1049920019,1050730019,1051540019,12910750019,
%T 13960510019,14167870019,67252030019,67252840019,67318450019,
%U 196918450019,197968210019,568118770019,568119580019,938270140019,938477500019
%N a(1)=2; a(n) is the smallest prime such that a(n)-a(n-1) is a 4th power (>0).
%C All members after 19 will end in '0019'.
%C Also, for n > 3, a(n) - a(n - 1) = k^4, k is a multiple of 30. - _Zak Seidov_, Apr 09 2013
%e a(3)=19, for 19 +k^4 to be prime, k must be even and divisible by 5. 19+10^4=10019=43*233,but 19+20^4 is prime.
%t Join[{2,3,19,p=160019},Table[x=30;While[!PrimeQ[q=p+x^4],x=x+30];p=q,{19}]] (* _Zak Seidov_, Apr 09 2013 *)
%Y Cf. A073609, A076201.
%K nonn
%O 1,1
%A _John L. Drost_, May 31 2005