A375171 Square array T(n,k), n>0 and k>0, read by antidiagonals in ascending order, giving the smallest n*k-digit number that, if arranged in an n X k matrix, form k-digit reversible prime in each row and n-digit reversible prime in each column, or -1 if no such number exists.

2, 37, 37, 337, 1111, 337, 3257, 111331, 113131, 3257, 32233, 13139731, 113101311, 11933371, 32233, 322573, 1111179779, 113101929311, 119310213191, 1119711779, 322573, 3222223, 111111131397, 113101167919739, 1193100990013911, 111971042937997, 111119111337, 3222223

Offset: 1

Author

Jean-Marc Rebert, Aug 06 2024

Keywords

• tabl
• base
• nonn

Examples

			T(3,2) = 111331 is the smallest 3*2-digit number that if arranged in a 3 X 2 matrix yields in each row and column an reversible prime, i.e.,
  11
  13
  31
-> 11 (1 time), 13 (1 time), 31 (1 time), 113 (1 time), 131 (1 time) are all reversible primes.
Table begins (upper left corner = T(1,1)):
     2       37          337             3257 ...
    37     1111       113131         11933371 ...
   337   111331    113101311     119310213191 ...
  3257 13139731 113101929311 1193100990013911 ...
   ...      ...          ...              ... ...
		

Crossrefs

Cf. A007500, A048054, A177513, A224164, A375234.

Programs

PARI

isp(x) = ispseudoprime(x) && ispseudoprime(fromdigits(Vecrev(digits((x)))));
ispd(x) = ispseudoprime(fromdigits(x)) && ispseudoprime(fromdigits(Vecrev(x)));
vp(n) = select(isp, [10^(n-1)..10^n-1]);
isok(val, n, k) = my(d=digits(val), v=vector(k, i, []), j=1); for (i=1, #d, v[j] = concat(v[j], d[i]); j++; if (j>k, j=1);); for (i=1, k, if (!ispd(v[i]), return(0));); return(1);
T(n,k) = my(v = vp(k), nbp = #v, nb = nbp^n); for (i=0, nb-1, my(d=digits(i, nbp)); if (d==[], d=vector(n)); while(#d x+1, d); my(s=""); for (i=1, #d, s = concat(s, Str(v[d[i]]))); my(val = eval(s)); if (isok(val, n, k), return(val));); \\ Michel Marcus, Aug 08 2024

Formula

T(1,n) = T(n,1) <= A177513(n) for n >1.

T(1,n) = T(n,1) = A177513(n) for n = 2..6.