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

1,5

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

Links

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

Example

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.

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

Crossrefs

Cf. A224748, A224908.

Sequence in context: A070306 A355639 A050378 * A161833 A294100 A139318

Adjacent sequences: A225213 A225214 A225215 * A225217 A225218 A225219

Keyword

nonn,base

Author

Jayanta Basu, May 02 2013

Status

approved