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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. 14
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

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-Fran├žois 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 A318926 A040120

Adjacent sequences:  A262366 A262367 A262368 * A262370 A262371 A262372

KEYWORD

nonn,base,tabl,look

AUTHOR

Alois P. Heinz, Sep 20 2015

STATUS

approved

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Last modified April 5 13:34 EDT 2020. Contains 333241 sequences. (Running on oeis4.)