A077345 a(n) is the n-th prime whose decimal expansion begins with the decimal expansion of n.

11, 23, 37, 401, 509, 617, 719, 829, 953, 1033, 1171, 1279, 1373, 1483, 15013, 1697, 17021, 18049, 19001, 20051, 21067, 22031, 23027, 24097, 25127, 26107, 27103, 28123, 29153, 30161, 31159, 32189, 33161, 34259, 35171, 36241, 37243, 38299, 39241, 40237, 41263

Offset: 1

Author

Amarnath Murthy, Nov 05 2002

Keywords

• base
• easy
• nonn

Comments

Original name was: Final terms of rows in A077344.

Subsidiary sequence: There can be a rearrangement of primes in groups so that the n-th group contains n primes beginning with n and not occurring earlier. E.g. the initial term of row 11 would be 113 and not 11.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000
• Index entries for primes involving decimal expansion of n

Crossrefs

Cf. A077344.

Main diagonal of A262369.

Programs

Maple

u:= (h, t)-> select(isprime, [seq(h*10^t+k, k=0..10^t-1)]):
A:= proc(n, k) local l, p;
      l:= proc() [] end; p:= proc() -1 end;
      while nops(l(k)) A(n$2):
seq(a(n), n=1..45);  # Alois P. Heinz, Sep 30 2015

Mathematica

u[h_, t_] := Select[Table[h*10^t + k, {k, 0, 10^t - 1}], PrimeQ];
A[n_, k_] := Module[{l, p}, l[] = {}; p[] = -1; While[Length[l[k]] < n, p[k] = p[k] + 1; l[k] = Join[l[k], u[k, p[k]]]]; l[k][[n]]];
a[n_] := A[n, n];
Table[a[n], {n, 1, 45}] (* Jean-François Alcover, Oct 25 2021, after Alois P. Heinz *)

Extensions

More terms and new name from Alois P. Heinz, Sep 30 2015