A065112 Smallest prime whose decimal expansion ends (nontrivially) with the n-th prime; or 0 if no such prime exists.

0, 13, 0, 17, 211, 113, 317, 419, 223, 229, 131, 137, 241, 443, 347, 353, 359, 461, 167, 271, 173, 179, 283, 389, 197, 5101, 1103, 5107, 1109, 2113, 4127, 2131, 2137, 4139, 11149, 1151, 4157, 1163, 3167, 6173, 2179, 1181, 3191, 1193, 5197, 6199, 4211

Offset: 1

Author

Robert G. Wilson v, Nov 12 2001

Keywords

• nonn
• base

Comments

a(1) and a(3) (respectively for primes 2 and 5) are trivially zero. All other terms are nonzero by Dirichlet's theorem on arithmetic progressions. - Joerg Arndt, Jun 06 2021

Links

• Daniel Mondot, Table of n, a(n) for n = 1..10000
• Wikipedia, Dirichlet's theorem on arithmetic progressions

Crossrefs

Cf. A030670.

Programs

Mathematica

f[n_] := (k = 1; While[a = ToExpression[ ToString[k] <> ToString[n]]; ! PrimeQ[a], k++ ]; a); Table[ f[ Prime[n]], {n, 4, 50} ]