The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A272376 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A272376

Twin primes both of which are the sum of three positive cubes.
(history; published version)

#20 by N. J. A. Sloane at Wed May 04 19:21:33 EDT 2016

STATUS

editing

approved

#19 by N. J. A. Sloane at Wed May 04 19:21:30 EDT 2016

NAME

Twin primes pairs whose members are both of which are the sum of three positive cubes.

STATUS

proposed

editing

#18 by Charles R Greathouse IV at Fri Apr 29 22:53:56 EDT 2016

STATUS

editing

proposed

Discussion

Sat Apr 30

04:59

Michel Marcus: pari gives different terms depending on the limit lim; for instance lim=100 gives 73, but lim=1000 gives 953, etc ...

#17 by Charles R Greathouse IV at Fri Apr 29 22:53:38 EDT 2016

LINKS

Charles R Greathouse IV, <a href="/A272376/b272376.txt">Table of n, a(n) for n = 1..10000</a>

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) && (isprime(t-2) || isprime(t+2)), , 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

STATUS

proposed

editing

#16 by Altug Alkan at Fri Apr 29 14:49:35 EDT 2016

STATUS

editing

proposed

#15 by Altug Alkan at Fri Apr 29 14:49:18 EDT 2016

CROSSREFS

Cf. A001097, A007490, A270225.

STATUS

proposed

editing

#14 by Giovanni Resta at Fri Apr 29 02:55:54 EDT 2016

STATUS

editing

proposed

Discussion

Fri Apr 29

03:03

Altug Alkan: Pari should be adopted, I think. Best regards.

#13 by Giovanni Resta at Fri Apr 29 02:55:34 EDT 2016

NAME

Twin primes that pairs whose members are both the sum of three positive cubes.

#12 by Charles R Greathouse IV at Fri Apr 29 01:17:50 EDT 2016

EXAMPLE

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

Discussion

Fri Apr 29

01:18

Charles R Greathouse IV: I get very different numbers: 3, 17, 29, 43, 73, 179, 197, 281, 349, 433, 521, 811, 857, 881, 1051, 1091, 1483, 2027, 2087, 2267, 2269, 2339, 2689, 2729, 2789, 2969, 3257, 3331, 3391, 3527, 3529, 3581, 4229, 4339, 4421, 4519, 4787, 4967, 5641, 5653, 5851, 5867, 6271, 6301, 6553

02:54

Giovanni Resta: Charles, I think it's because Carmine want both twin primes to be sum of 3 positive cubes. So 3 is not in the list because 5 is not a sum of 3 cubes. I will change the name.

#11 by Charles R Greathouse IV at Fri Apr 29 01:17:31 EDT 2016

EXAMPLE

a(3)=3527, a(4)= and 3529 since 3527=3^3+5^3+15^3 and 3529=1^3+11^3+13^3.

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) && (isprime(t-2) || isprime(t+2)), listput(v, t))))); Set(v) \\ Charles R Greathouse IV, Apr 29 2016

STATUS

proposed

editing