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

1,1

Links

Table of n, a(n) for n=1..28.

Formula

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

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

Example

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 ...
 ...      ... 	     ...              ... ...

Prog

(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 <n, d=concat(0, d)); d = apply(x->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

Crossrefs

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

Sequence in context: A178200 A049106 A346067 * A290803 A042569 A066196

Adjacent sequences: A375168 A375169 A375170 * A375172 A375173 A375174

Keyword

tabl,base,nonn

Author

Jean-Marc Rebert, Aug 06 2024

Status

approved