A353550 Primes having cube prime gaps to both neighbor primes.

89689, 107441, 367957, 368021, 725209, 803749, 832583, 919511, 1070753, 1315151, 1333027, 1353487, 1414913, 1843357, 2001911, 2038039, 2201273, 2207783, 2269537, 2356699, 2356763, 2670817, 2696843, 2715071, 2717929, 2731493, 2906887, 2971841, 3032467, 3184177, 3252217

Offset: 1

Author

Karl-Heinz Hofmann, Apr 25 2022

Keywords

• nonn

Comments

Up to prime 669763117 all gaps are 8 and 64 or 64 and 8. Prime 669763117 is the first one with gaps 8 and 216. Possible gaps must be in A016743.

Examples

			a(2) = 107441; previous prime is 107377 and the gap is 64 (a cube); next prime is 107449 and the gap is 8 (a cube too).
		

Links

• Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A000578, A016743, A353088 (square gaps), A163112 (gaps > 20).

Cf. A353137 (gaps are a power of 2), A353135 (Fibonacci gaps).

Cf. A353136 (triangular numbers gaps).

Programs

Maple

iscube:= proc(n) option remember; is(n=iroot(n, 3)^3) end:
q:= n-> isprime(n) and andmap(iscube, [n-prevprime(n), nextprime(n)-n]):
select(q, [$3..3500000])[];  # Alois P. Heinz, Apr 25 2022

Mathematica

p = Prime[Range[3*10^5]]; pos = Position[Differences[p], ?(IntegerQ@Surd[#, 3] &)] // Flatten; p[[pos[[Position[Differences[pos], 1] // Flatten]] + 1]] (* _Amiram Eldar, Apr 26 2022 *)

Python

from sympy import sieve as p
def A016743(totest): return (totest % 2 == 0 and round(totest**(1/3))**3 == totest)
print([p[n] for n in range(2,235000) if A016743(p[n]-p[n-1]) and A016743(p[n+1]-p[n])])