A225216 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.

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

Offset: 1

Author

Jayanta Basu, May 02 2013

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A224748, A224908.

Programs

Mathematica

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