A075612 a(1) = 1, a(n) = smallest prime number not already used such that concatenation of a(k) and a(n) is composite for all k = 1 to n-1.

1, 2, 5, 17, 19, 43, 61, 127, 149, 199, 263, 349, 353, 461, 587, 769, 809, 883, 1009, 1303, 1619, 2179, 2207, 2467, 2591, 2593, 2909, 3019, 3517, 3821, 3853, 3989, 5669, 6121, 8011, 8273, 8563, 9127, 10163, 10639, 12781, 13009, 13577, 13619, 13907

Offset

1,2

Comments

Is the sequence finite? Surprisingly it contains the finite sequence A020608 (2,5,17,19,43,61).

Links

Table of n, a(n) for n=1..45.

Emmanuel Vantieghem, Table of n, a(n) for n = 1..306

Example

a(4) = 17 because 117, 217 and 517 are all composite.

Mathematica

(* to compute the terms up to B *)
K[m_Integer, n_Integer] := n + m 10^IntegerLength[n];
A = {1, 2}; i = 2; b = 2; While[b < B, i++; m = Last[A];
b = NextPrime[m]; flag = 0;
While[flag == 0, j = 1; While[j < i && ! PrimeQ[K[A[[j]], b]], j++];
  If[j == i, flag = 1; AppendTo[A, b],
   b = NextPrime[b]]]]; A (* Emmanuel Vantieghem, Nov 28 2015 *)

Crossrefs

Cf. A075611.

Sequence in context: A215276 A095287 A020608 * A156010 A215273 A041283

Adjacent sequences: A075609 A075610 A075611 * A075613 A075614 A075615

Keyword

base,nonn

Author

Amarnath Murthy, Sep 28 2002

Extensions

More terms from David Wasserman, Jan 21 2005

Status

approved