A155030 Primes p=A000040(n) with prime index n such that the concatenation n//p is a composite number.

5, 11, 17, 31, 41, 67, 109, 127, 157, 191, 211, 241, 277, 331, 367, 401, 461, 509, 547, 563, 587, 599, 617, 739, 773, 797, 859, 877, 919, 967, 991, 1031, 1063, 1087, 1153, 1171, 1201, 1217, 1297, 1409, 1447, 1471, 1499, 1523, 1597, 1621, 1669, 1723, 1741

Offset

1,1

Comments

Demanding that the index is not a prime would lead to A155025 instead.

Links

Table of n, a(n) for n=1..49.

Example

For the index n=3, a prime, p = prime(3)=5, the concatenation 35 is composite, so p=5 is added to the sequence.
For the index n=5, a prime, p = prime(5)=11, the concatenation 511 is composite, so p=11 is added to the sequence.
For the index n=6, not a prime, nothing is added to the sequence.
For the index n=7, a prime, p = prime(7)=17, the concatenation 717 is composite, so p=17 is added to the sequence.

Mathematica

Prime[#]&/@Select[Prime[Range[70]], CompositeQ[FromDigits[Join[ IntegerDigits[ #], IntegerDigits[ Prime[#]]]]]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 14 2019 *)

Crossrefs

Cf. A000027, A000040, A002808, A155025.

Sequence in context: A088046 A155882 A087373 * A030468 A277290 A085634

Adjacent sequences: A155027 A155028 A155029 * A155031 A155032 A155033

Keyword

nonn,base

Author

Juri-Stepan Gerasimov, Jan 19 2009

Extensions

Definition clarified, sequence extended by R. J. Mathar, Oct 14 2009

Status

approved