A262369 - OEIS

%I #22 Nov 11 2020 19:08:00

%S 11,2,13,3,23,17,41,31,29,19,5,43,37,211,101,61,53,47,307,223,103,7,

%T 67,59,401,311,227,107,83,71,601,503,409,313,229,109,97,89,73,607,509,

%U 419,317,233,113,101,907,809,79,613,521,421,331,239,127

%N A(n,k) is the n-th prime whose decimal expansion begins with the decimal expansion of k; square array A(n,k), n>=1, k>=1, read by antidiagonals.

%H Alois P. Heinz, <a href="/A262369/b262369.txt">Antidiagonals n = 1..200, flattened</a>

%H <a href="/index/Pri#piden">Index entries for primes involving decimal expansion of n</a>

%e Square array A(n,k) begins:

%e :  11,   2,   3,  41,   5,  61,   7,  83, ...

%e :  13,  23,  31,  43,  53,  67,  71,  89, ...

%e :  17,  29,  37,  47,  59, 601,  73, 809, ...

%e :  19, 211, 307, 401, 503, 607,  79, 811, ...

%e : 101, 223, 311, 409, 509, 613, 701, 821, ...

%e : 103, 227, 313, 419, 521, 617, 709, 823, ...

%e : 107, 229, 317, 421, 523, 619, 719, 827, ...

%e : 109, 233, 331, 431, 541, 631, 727, 829, ...

%p u:= (h, t)-> select(isprime, [seq(h*10^t+k, k=0..10^t-1)]):

%p A:= proc(n, k) local l, p;

%p       l:= proc() [] end; p:= proc() -1 end;

%p       while nops(l(k))<n do p(k):= p(k)+1;

%p         l(k):= [l(k)[], u(k, p(k))[]]

%p       od: l(k)[n]

%p     end:

%p seq(seq(A(n, 1+d-n), n=1..d), d=1..12);

%t u[h_, t_] := Select[Table[h*10^t + k, {k, 0, 10^t - 1}], PrimeQ];

%t 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 Table[Table[A[n, 1+d-n], {n, 1, d}], {d, 1, 12}] // Flatten (* _Jean-François Alcover_, Dec 06 2019, from Maple *)

%Y Columns k=1-9 give: A045707, A045708, A045709, A045710, A045711, A045712, A045713, A045714, A045715.

%Y Row n=1 gives A018800.

%Y Main diagonal gives A077345.

%Y Cf. A077344, A262365.

%K nonn,base,tabl,look

%O 1,1

%A _Alois P. Heinz_, Sep 20 2015