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

1,1

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

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))<n do p(k):= p(k)+1;
        l(k):= [l(k)[], u(k, p(k))[]]
      od: l(k)[n]
    end:
a:= n-> 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 *)

Crossrefs

Cf. A077344.

Main diagonal of A262369.

Sequence in context: A275591 A250665 A339080 * A130282 A019356 A046440

Adjacent sequences: A077342 A077343 A077344 * A077346 A077347 A077348

Keyword

base,easy,nonn

Author

Amarnath Murthy, Nov 05 2002

Extensions

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

Status

approved