A249628 Sums of two numbers that are the average of a twin prime pair (A014574).

8, 10, 12, 16, 18, 22, 24, 30, 34, 36, 42, 46, 48, 54, 60, 64, 66, 72, 76, 78, 84, 90, 102, 106, 108, 112, 114, 120, 126, 132, 138, 142, 144, 150, 154, 156, 162, 168, 174, 180, 184, 186, 192, 196, 198, 202, 204, 210, 216, 222, 228, 232, 234, 240, 244, 246, 252

Offset: 1

Author

Wesley Ivan Hurt, Nov 02 2014

Keywords

• nonn

Comments

The addends need not be distinct, see example.

Probably a(n) ~ 6n and all multiples of 6 greater than 4206 are present. - Charles R Greathouse IV, Nov 06 2014

Examples

			8 is in the sequence since 8 = 4+4 and 4 is the average of the twin primes 3 and 5.
10 is in the sequence since 10 = 4+6 and both 4 and 6 are the average of the twin primes 3,5 and 5,7 respectively.
12 is in the sequence since 12 = 6+6 and 6 is the average of the twin primes 5 and 7.
14 is not in the sequence since it is not the sum of two numbers that are the average of twin primes.
		

Links

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

Crossrefs

Cf. A014574 (average of twin prime pairs).

Programs

PARI

v=[];for(n=1,10^3,if(isprime(n-1)&&isprime(n+1),v=concat(v,n)))
b=[];for(n=1,1000,for(k=1,n,if(vecsearch(v,k)&&vecsearch(v,n-k),b=concat(b,n))));vecsort(b,,8) \\ Derek Orr, Nov 02 2014

PARI

list(lim)=my(v=List(),p,r); p=3; forprime(q=5,lim-3, if(q-p>2, p=q; next); r=3; forprime(s=5,min(lim-q+2,q), if(s-r==2, listput(v, p+s)); r=s); p=q); Set(v) \\ Charles R Greathouse IV, Nov 06 2014

PARI

list(lim)=my(v=List(),P=primes([3,lim\1-3]),Q=v,t); for(i=2,#P, if(P[i]-P[i-1]==2, listput(Q,P[i]-1))); P=0; forstep(n=8,lim,2, for(i=1,#Q, if(setsearch(Q,t=n-Q[i]), listput(v,n); break); if(tCharles R Greathouse IV, Nov 06 2014

PARI

is(n)=my(p=3);forprime(q=5,n\2+1,if(isprime(n-p)&&isprime(n-p-2),return(1));p=q);0 \\ Charles R Greathouse IV, Nov 06 2014

Extensions

Missing a(19) added by Charles R Greathouse IV, Nov 06 2014