A155025 Primes p=A000040(n) with nonprime index n such that the concatenation n//p is a composite number.
2, 19, 23, 29, 43, 47, 53, 71, 73, 79, 89, 97, 101, 107, 131, 137, 139, 163, 167, 173, 193, 223, 227, 229, 233, 239, 257, 281, 293, 307, 311, 313, 317, 337, 347, 349, 359, 373, 379, 383, 389, 397, 409, 419, 433, 443, 449, 457, 463, 467, 491, 499, 503, 521, 541, 557, 569
Offset: 1
Examples
For the nonprime n=1, p = prime(n) = 2, the concatenation is 12 is composite, and p is added to the sequence. For the nonprime n=8, p = prime(8) = 19, the concatenation 819 is composite, and p=19 is added to the sequence. For the nonprime n=12, p = prime(12) = 37, the concatenation 1237 is prime, so p=37 is not added to the sequence.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..10000
Programs
-
Mathematica
cnQ[{n_,p_}]:=!PrimeQ[n]&&!PrimeQ[FromDigits[Flatten[ IntegerDigits/@ {n,p}]]]; Transpose[Select[Table[{n,Prime[n]},{n,150}],cnQ]][[2]] (* Harvey P. Dale, Dec 18 2012 *)
Extensions
Definition clarified, sequence extended by R. J. Mathar, Oct 14 2009