A276831 -id:A276831 - cp's OEIS frontend

A277118 For a lesser p of twin primes, let B_k be A159559, but with initial term k; then a(n) is the smallest m such that B_(p+2)(m)-B_p(m)>6, where p = A001359(n-1), or a(n) = 0 if there is no such m.

0, 13, 0, 0, 0, 9, 0, 11, 11, 5, 3, 15, 3, 7, 3, 0, 3, 0, 3, 5, 7, 3, 11, 5, 3, 5, 11, 3, 9, 3, 3, 7, 3, 5, 5, 3, 5, 3, 5, 11, 3, 5, 0, 0, 5, 5, 7, 5, 13, 7, 0, 5, 3, 3, 3, 3, 7, 3, 3, 3, 5, 3, 7, 3, 3, 0, 3, 5, 5, 3, 11, 11, 5, 3, 5, 7, 5, 3, 0, 3, 3, 3, 3, 3

Offset: 2

Vladimir Shevelev and Peter J. C. Moses, Sep 30 2016

nonn

Theorem: a(n) takes only the values 0, 3, 5, 7, 9, 11, 13, 15, and 17.

Peter J. C. Moses, Table of n, a(n) for n = 2..5001
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.

Cf. A022009, A159559, A229019, A276676, A276703, A276767, A276826, A276831, A276848.

nextcomposite(n)=if(n<4, return(4)); n=ceil(n); if(isprime(n), n+1, n)
do(p)=my(a=p,b=p+2,f); for(n=3,17, f=if(isprime(n), nextprime, nextcomposite); a=f(a+1); b=f(b+1); if(b-a > 6, return(n))); 0
p=2; forprime(q=3,1e3, if(q-p==2, print1(do(p)", ")); p=q) \\ Charles R Greathouse IV, Oct 17 2016

a(n) = 3 on a subsequence of measure 1. - Charles R Greathouse IV, Oct 17 2016

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.

Original entry on oeis.org

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

Vladimir Shevelev, Sep 21 2016

nonn

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.

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.

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

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

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

cp's OEIS Frontend

A277118 For a lesser p of twin primes, let B_k be A159559, but with initial term k; then a(n) is the smallest m such that B_(p+2)(m)-B_p(m)>6, where p = A001359(n-1), or a(n) = 0 if there is no such m.

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