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

34, 12025, 12130, 22789, 102952, 103039, 205222, 226019, 300176, 492203, 492221, 570760, 1030144, 1224376, 1224466, 2570470, 2684090, 3307264, 3868067, 3868157, 4329380, 4656049, 4656427, 5176537, 6966262, 6966403, 6966421, 7186697, 7186787, 7187318, 7187516, 7644406, 11694973, 12007691, 12008315

Offset: 1

Author

Will Gosnell and Robert Israel, Oct 11 2019

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2400

Crossrefs

Cf. A030078, A055012, A179239.

Programs

Maple

filter:= proc(n) local x,t,F;
  if isprime(n) then return false fi;
  x:= n + add(t^3, t = convert(n,base,10));
  F:= ifactors(x)[2];
  nops(F)=1 and F[1][2]=3
end proc:
F:= proc(p,lastp) local n0;
  n0:= max(p^3 - 9^3*(1+ilog10(p^3)),lastp^3+1);
  select(filter, [$n0 .. p^3]);
end proc:
seq(op(F(ithprime(i),ithprime(i-1))),i=2..50);

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