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A353550
Primes having cube prime gaps to both neighbor primes.
2
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
1,1
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.
LINKS
EXAMPLE
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).
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 *)
PROG
(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])])
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).
Sequence in context: A205898 A250452 A204670 * A359291 A236908 A331354
KEYWORD
nonn
AUTHOR
Karl-Heinz Hofmann, Apr 25 2022
STATUS
approved