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A076201 a(n), for n > 1, equals the least prime p such that p - a(n-1) is a cube, a(1)=2.

%I A076201 #14 Aug 13 2025 13:50:23
%S A076201 2,3,11,19,83,1811,2027,2243,2251,2467,2531,2539,3539,3547,4547,5059,
%T A076201 10891,12619,13619,13627,13691,13907,14419,155027,155539,156539,
%U A076201 157051,267643,268643,270371,270379,270443,270451,270667,276499,277499,280243,281243,281251
%N A076201 a(n), for n > 1, equals the least prime p such that p - a(n-1) is a cube, a(1)=2.
%H A076201 Zak Seidov, <a href="/A076201/b076201.txt">Table of n, a(n) for n = 1..1000</a>
%e A076201 a(2) = 3 because 3 - a(1) = 1^3.
%e A076201 a(3) = 11 because 11 - a(2) = 2^3, while neither 5 - 3 nor 7 - 3 is a cube.
%t A076201 p = 3; s = Join[{2, 3}, Table[x = 2; While[!PrimeQ[q = p + x^3], x = x + 2]; p = q, {29}]] (* _Zak Seidov_, Apr 08 2013 *)
%t A076201 nxt[a_]:=Module[{p=NextPrime[a]},While[!IntegerQ[CubeRoot[p-a]],p=NextPrime[p]];p]; NestList[nxt,2,40] (* _Harvey P. Dale_, Aug 13 2025 *)
%Y A076201 Cf. A073609.
%K A076201 nonn
%O A076201 1,1
%A A076201 _Zak Seidov_, Nov 02 2002