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

%I A077345 #15 Oct 25 2021 08:08:04
%S A077345 11,23,37,401,509,617,719,829,953,1033,1171,1279,1373,1483,15013,1697,
%T A077345 17021,18049,19001,20051,21067,22031,23027,24097,25127,26107,27103,
%U A077345 28123,29153,30161,31159,32189,33161,34259,35171,36241,37243,38299,39241,40237,41263
%N A077345 a(n) is the n-th prime whose decimal expansion begins with the decimal expansion of n.
%C A077345 Original name was: Final terms of rows in A077344.
%C A077345 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.
%H A077345 Alois P. Heinz, <a href="/A077345/b077345.txt">Table of n, a(n) for n = 1..1000</a>
%H A077345 <a href="/index/Pri#piden">Index entries for primes involving decimal expansion of n</a>
%p A077345 u:= (h, t)-> select(isprime, [seq(h*10^t+k, k=0..10^t-1)]):
%p A077345 A:= proc(n, k) local l, p;
%p A077345       l:= proc() [] end; p:= proc() -1 end;
%p A077345       while nops(l(k))<n do p(k):= p(k)+1;
%p A077345         l(k):= [l(k)[], u(k, p(k))[]]
%p A077345       od: l(k)[n]
%p A077345     end:
%p A077345 a:= n-> A(n$2):
%p A077345 seq(a(n), n=1..45);  # _Alois P. Heinz_, Sep 30 2015
%t A077345 u[h_, t_] := Select[Table[h*10^t + k, {k, 0, 10^t - 1}], PrimeQ];
%t A077345 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]]];
%t A077345 a[n_] := A[n, n];
%t A077345 Table[a[n], {n, 1, 45}] (* _Jean-François Alcover_, Oct 25 2021, after _Alois P. Heinz_ *)
%Y A077345 Cf. A077344.
%Y A077345 Main diagonal of A262369.
%K A077345 base,easy,nonn
%O A077345 1,1
%A A077345 _Amarnath Murthy_, Nov 05 2002
%E A077345 More terms and new name from _Alois P. Heinz_, Sep 30 2015