A225216 - OEIS

%I #9 May 03 2013 02:19:48

%S 0,1,0,1,2,1,2,2,4,2,2,2,4,1,4,5,4,3,4,5,6,4,5,5,6,5,6,5,3,8,4,6,8,7,

%T 8,7,5,6,8,8,4,9,7,5,10,5,9,5,8,8,10,8,8,14,10,7,14,8,8,11,10,13,8,10,

%U 10,10,11,12,13,8,11,14,12,11,13,13,13,16

%N Let p = n-th prime. Then a(n) = number of primes generated by prepending to the digits of p the digits of q, where q is any prime less than p.

%C The graph makes it apparent that there are fewer primes generated when the prime p increases its length from 3 to 4 and 4 to 5 digits. - _T. D. Noe_, May 03 2013

%H T. D. Noe, <a href="/A225216/b225216.txt">Table of n, a(n) for n = 1..10000</a>

%e a(2)=1 since second prime 3 generates 23. Also a(7)=2 since for the seventh prime 17 we have two primes 317 and 1117.

%t con[x_,y_] := FromDigits[Join[IntegerDigits[Prime[x]], IntegerDigits[Prime[y]]]]; t={}; Do[c=0; Do[If[PrimeQ[con[i,n]], c=c+1], {i,n}]; AppendTo[t,c], {n,78}]; t

%Y Cf. A224748, A224908.

%K nonn,base

%O 1,5

%A _Jayanta Basu_, May 02 2013