A334885 Let q = p | p' be the digit concatenation of a prime p with its prime successor. If the result is a prime repeat the construction setting p = q. a(n) is the smallest prime for which this can be repeated exactly n times.

3, 2, 13681, 467, 127787377, 200603842261

Offset: 0

Author

Giovanni Resta, May 14 2020

Keywords

• nonn
• base
• more

Comments

a(6) > 10^13.

Examples

			Let "|" denote concatenation.
3 | 5 = 35, which is not prime, so a(0) = 3.
2 | 3 = 23 (prime), 23 | 29 = 2329 (composite), so a(1) = 2.
13681 | 13687 (prime), 1368113687 | 1368113699 (prime), 13681136871368113699 | 13681136871368113711 (composite), so a(2) = 13681.
		

Links

• Carlos Rivera, Puzzle 29. P_i = P_(i-1) & nxtprm(P_(i-1)), P_i = prime for i => 1, The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A030459, A034593, A036339, A036340, A036341.

Programs

Mathematica

a[n_] := Block[{pp=1, p, q, c=-1}, While[ c!=n, c=0; p = pp = NextPrime@ pp; While[ PrimeQ[ q = FromDigits[ Join @@ IntegerDigits@{p, NextPrime@ p}]], c++; p = q]]; pp]; a /@ Range[0, 3]