A235109 Averages q of twin prime pairs, such that q concatenated to q is also the average of a twin prime pair.

42, 102, 108, 180, 192, 270, 312, 420, 522, 660, 822, 882, 1230, 1482, 4242, 4788, 8820, 10332, 11550, 13692, 14550, 14562, 14868, 15732, 17910, 18522, 20550, 21648, 22620, 23670, 23832, 26262, 27738, 35838, 38922, 39042, 40128, 42018, 43962, 44532, 46440

Offset: 1

Author

Michael G. Kaarhus, Jan 03 2014

Keywords

• base
• nonn

Examples

			192 is in this sequence, because 192 is an average of a twin prime pair, and so is 192192.
		

Links

• Michael G. Kaarhus, Table of n, a(n) for n = 1..770

Crossrefs

Subsequence of A014574.

Programs

Maxima

q:0$ for n:1 thru 800 step 0 do (q:q+6, if(primep(q-1) and primep(q+1)) then (b:concat(q,q), c:eval_string(b), if(primep(c-1) and primep(c+1)) then (if c>341550071728321 then (print("# ", c, " not determ."), n:5000), print(n, ", ", q), n:n+1 ) ) )$

PARI

cat(n)=eval(concat(Str(n),n))
istwin(n)=n%6==5&&isprime(n)&&isprime(n+2)
v=List();p=2;forprime(q=3,1e10,if(q-p==2 && istwin(cat(p+1)-1), listput(v,p+1); if(#v==10^4,return));p=q) \\ Charles R Greathouse IV, Jan 03 2014