A272376 Twin primes both of which are the sum of three positive cubes.

2267, 2269, 3527, 3529, 10331, 10333, 14867, 14869, 17207, 17209, 18521, 18523, 18917, 18919, 20231, 20233, 20357, 20359, 25577, 25579, 27791, 27793, 28547, 28549, 31247, 31249, 35279, 35281, 36899, 36901, 40697, 40699, 44279, 44281, 48779, 48781, 51479, 51481

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

3527 and 3529 are terms since 3527=3^3+5^3+15^3 and 3529=1^3+11^3+13^3.

Mathematica

cu[n_] := {}!=Quiet@ IntegerPartitions[n, {3}, Range[n^(1/3)]^3, 1]; Flatten@ Rest@ Reap@ Do[If[ PrimeQ[p+2] && cu[p] && cu[p+2], Sow[{p, p+2}]], {p, Prime@ Range@ 10000}] (* Giovanni Resta, Apr 28 2016 *)

Prog

(PARI) list(lim)=my(v=List(), k, t); lim\=1; for(x=1, sqrtnint(lim-2, 3), for(y=1, min(sqrtnint(lim-x^3-1, 3), x), k=x^3+y^3; for(z=1, min(sqrtnint(lim-k, 3), y), if(isprime(t=k+z^3), listput(v, t))))); v=Set(v); for(i=2, #v-1, if(v[i]!=v[i-1]+2 && v[i]!=v[i+1]-2, v[i]=0)); v=Set(v); v[3..#v] \\ Charles R Greathouse IV, Apr 29 2016

Crossrefs

Cf. A001097, A007490, A270225.

Sequence in context: A251509 A263972 A263963 * A288883 A206212 A154673

Adjacent sequences: A272373 A272374 A272375 * A272377 A272378 A272379

Keyword

nonn

Author

Carmine Suriano, Apr 28 2016

Status

approved