A262369 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.

11, 2, 13, 3, 23, 17, 41, 31, 29, 19, 5, 43, 37, 211, 101, 61, 53, 47, 307, 223, 103, 7, 67, 59, 401, 311, 227, 107, 83, 71, 601, 503, 409, 313, 229, 109, 97, 89, 73, 607, 509, 419, 317, 233, 113, 101, 907, 809, 79, 613, 521, 421, 331, 239, 127

Offset

1,1

Links

Alois P. Heinz, Antidiagonals n = 1..200, flattened

Index entries for primes involving decimal expansion of n

Example

Square array A(n,k) begins:
:  11,   2,   3,  41,   5,  61,   7,  83, ...
:  13,  23,  31,  43,  53,  67,  71,  89, ...
:  17,  29,  37,  47,  59, 601,  73, 809, ...
:  19, 211, 307, 401, 503, 607,  79, 811, ...
: 101, 223, 311, 409, 509, 613, 701, 821, ...
: 103, 227, 313, 419, 521, 617, 709, 823, ...
: 107, 229, 317, 421, 523, 619, 719, 827, ...
: 109, 233, 331, 431, 541, 631, 727, 829, ...

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

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]]];
Table[Table[A[n, 1+d-n], {n, 1, d}], {d, 1, 12}] // Flatten (* Jean-François Alcover, Dec 06 2019, from Maple *)

Crossrefs

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

Row n=1 gives A018800.

Main diagonal gives A077345.

Cf. A077344, A262365.

Sequence in context: A318927 A267320 A303785 * A092260 A370004 A318926

Adjacent sequences: A262366 A262367 A262368 * A262370 A262371 A262372

Keyword

nonn,base,tabl,look

Author

Alois P. Heinz, Sep 20 2015

Status

approved