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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A318202 Prime numbers p such that p-3 cannot be written as sum of two twin prime numbers (not necessarily forming a pair of twin primes).

Original entry on oeis.org

2, 3, 5, 7, 97, 101, 521, 787, 907, 911, 1117, 1151, 1361, 3251, 4211
Offset: 1

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Author

Dimitris Valianatos, Aug 21 2018

Keywords

Comments

Conjecture 1: All prime numbers >= 11 can be written as sum of 3 twin prime numbers.
Conjecture 2: All prime numbers aside from the 15 terms given here can be written as a sum of three twin prime numbers with (at least) one of them equal to 3.
If the sequence is finite then there are infinitely many twin primes.
For the terms in this sequence, the lexicographically least partitions into three twin primes are: 97=5+19+73, 101=11+17+73, 521=11+197+313, 787=5+139+643, 907=5+19+883, 911=11+17+883, 1117=5+19+1093, 1151=11+107+1033, 1361=11+29+1321, 3251=11+71+3169, 4211=11+41+4159.
a(16) > 10^6 if it exists. - Amiram Eldar, Dec 06 2018

Examples

			a(6) = 101 because 101 - 3 = 98 and (98 - 73 = 25, 98 - 71 = 27), (98 - 61 = 37, 98 - 59 = 39), ..., (98 - 5 = 93, 98 - 3 = 95) aren't twin primes.

Links

Crossrefs

Cf. A000040, A001097, A007534, A129363, A321221.

Programs

  • Mathematica
    p = Prime[Range[600]]; p2 = Select[p, PrimeQ[# - 2] || PrimeQ[# + 2] &]; Select[ p - 3, IntegerPartitions[#, {2}, p2] == {} &] + 3 (* Amiram Eldar, Nov 15 2018 *)
  • PARI
    {forprime(n=2,10^4,p=n-3;forprime(t1=2,n,forprime(t2=t1,n,t12=t1+t2; if((isprime(t1-2)||isprime(t1+2))&&(isprime(t2-2)||isprime(t2+2)), if(t12==p,break(2)))));if(t12==2*n,print1(n", ")))}
  • PARI
    isok(p) = {if (isprime(p), p -= 3; forprime(q = 2, p, if (isprime(r=p-q), if ((isprime(r+2) || isprime(r-2)) && (isprime(q-2) || isprime(q+2)), return (0)););); return (1));} \\ Michel Marcus, Dec 05 2018
  • PARI
    \\ See Corneth link \\ David A. Corneth, Dec 05 2018

Extensions

2,3,5,7 prepended by David A. Corneth, Dec 05 2018
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