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%I #27 Jul 01 2018 16:33:31
%S 2,727,2017,11807,15193,39679,70913,124199,314777,1090151,1895833,
%T 3017167,4982833,8841167,10841833,14570351,17587081,24557111,26095889,
%U 27061487,32257513,45051263,46073737,61776439,72441289,74756663,82707337,114430031,157667761,170841239
%N a(1) = 2; a(n) is the smallest prime > a(n-1) such that a(n) + a(n-1) is a cube.
%H Zak Seidov, <a href="/A062066/b062066.txt">Table of n, a(n) for n = 1..10000</a> (first 45 terms from Harry J. Smith)
%e The next term after 727 is 2017 as 727 + 2017 = 2744 = 14^3.
%t a=2;s={a};c=1;k=1;Do[Label[ne];If[PrimeQ[b=k^3-a]&&b>a,a=b;c++;AppendTo[s,a];If[c==10000, Break[]]];k++;Goto[ne],{1}];s (*Zak Seidov, Sep 28 2011*)
%t sp[n_]:=Module[{c=Floor[Surd[NextPrime[2n],3]]+1},While[!PrimeQ[ c^3- n], c++];c^3-n]; NestList[sp,2,30] (* _Harvey P. Dale_, Dec 19 2015 *)
%o (PARI) iscube(x)= { f=factor(x)~; for(i=1, length(f), if (t=f[2, i]%3, return(0))); return(1); } { a=2; for (n=1, 45, a1=a; if (n>1, until (iscube(a + a1), a=nextprime(a + 1))); write("b062066.txt", n, " ", a) ) } \\ _Harry J. Smith_, Jul 31 2009
%Y Cf. A062064.
%K nonn
%O 1,1
%A _Amarnath Murthy_, Jun 12 2001
%E More terms from Larry Reeves (larryr(AT)acm.org), Jun 21 2001
%E Further terms from Philip Sung (phil(AT)main.nu), Sep 11 2001
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