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A328293 Composite numbers k such that k+A055012(k) is the cube of a prime.

%I A328293 #27 Jul 02 2021 01:56:15
%S A328293 34,12025,12130,22789,102952,103039,205222,226019,300176,492203,
%T A328293 492221,570760,1030144,1224376,1224466,2570470,2684090,3307264,
%U A328293 3868067,3868157,4329380,4656049,4656427,5176537,6966262,6966403,6966421,7186697,7186787,7187318,7187516,7644406,11694973,12007691,12008315
%N A328293 Composite numbers k such that k+A055012(k) is the cube of a prime.
%C A328293 Computing the range of A055012(n) up to some upper limit using A179239 might help reduce the search space for finding terms. - _David A. Corneth_, Oct 11 2019
%H A328293 Robert Israel, <a href="/A328293/b328293.txt">Table of n, a(n) for n = 1..2400</a>
%e A328293 a(3) = 12130 is included because 12130 is composite and 12130 + 1^3 + 2^3 + 1^3 + 3^3 + 0^3 = 12167 = 23^3 and 23 is prime.
%p A328293 filter:= proc(n) local x,t,F;
%p A328293   if isprime(n) then return false fi;
%p A328293   x:= n + add(t^3, t = convert(n,base,10));
%p A328293   F:= ifactors(x)[2];
%p A328293   nops(F)=1 and F[1][2]=3
%p A328293 end proc:
%p A328293 F:= proc(p,lastp) local n0;
%p A328293   n0:= max(p^3 - 9^3*(1+ilog10(p^3)),lastp^3+1);
%p A328293   select(filter, [$n0 .. p^3]);
%p A328293 end proc:
%p A328293 seq(op(F(ithprime(i),ithprime(i-1))),i=2..50);
%o A328293 (PARI) (scan(a,b)=forcomposite(n=max(a,b-9^3*(logint(b,10)+1))+1,b, n+A055012(n)==b && printf(n","))); forprime(p=1+o=2,234, scan(o^3,p^3)) \\ _M. F. Hasler_, Oct 11 2019
%Y A328293 Cf. A030078, A055012, A179239.
%K A328293 nonn,base
%O A328293 1,1
%A A328293 _Will Gosnell_ and _Robert Israel_, Oct 11 2019