A276848 For a lesser p of twin primes, let B_(p+2) and B_p be sequences defined as A159559, but with initial terms p+2 and p respectively. The sequence lists p for which all differences B_(p+2)(n)-B_p(n)<=6.

3, 11, 17, 29, 59, 227, 269, 1277, 1289, 1607, 2129, 2789, 3527, 3917, 4637, 4787, 5639, 8999, 13679, 14549, 18119, 27737, 36779, 38447, 39227, 44267, 62129, 71327, 75989, 80669, 83219, 88799, 93479, 97367, 99707, 113147, 113159, 115769, 122027, 122387, 124337, 124769, 132749, 150209, 160079

Offset: 1

Author

Vladimir Shevelev, Sep 21 2016

Keywords

• nonn

Comments

B_(p+2)(n) - B_p(n) < 6 for all n >= 2 if and only if p = 3.

It is astonishing that, although terms a(n) == 7 or 9 (mod 10) occur often, the first terms a(n)==1 (mod 10) are 11, 165701, ... (cf. A022009). This phenomenon is explained in the Shevelev link.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• Vladimir Shevelev, "nearest" twin primes, Post to seqfan, Sep 21 2016.
• Vladimir Shevelev, Peter J. C. Moses, Constellations of primes generated by twin primes, arXiv:1610.03385 [math.NT], 2016.

Crossrefs

Cf. A001359, A159559, A229019, A276676, A276703, A276767, A276826, A276831, A022009.

Programs

PARI

nextcomposite(n)=if(n<4, return(4)); n=ceil(n); if(isprime(n), n+1, n)
is(n)=if(!isprime(n) || !isprime(n+2), return(0)); my(p=n,q=n+2,k=2,f); while(p!=q && q-p<7, f=if(isprime(k++),nextprime,nextcomposite); p=f(p+1); q=f(q+1)); p==q \\ Charles R Greathouse IV, Sep 21 2016

Extensions

More terms from Peter J. C. Moses, Sep 21 2016