cp's OEIS Frontend

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.

%I A375171 #89 Apr 26 2025 20:12:21
%S A375171 2,37,37,337,1111,337,3257,111331,113131,3257,32233,13139731,
%T A375171 113101311,11933371,32233,322573,1111179779,113101929311,119310213191,
%U A375171 1119711779,322573,3222223,111111131397,113101167919739,1193100990013911,111971042937997,111119111337,3222223
%N 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.
%F A375171 T(1,n) = T(n,1) <= A177513(n) for n >1.
%F A375171 T(1,n) = T(n,1) = A177513(n) for n = 2..6.
%e A375171 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.,
%e A375171   11
%e A375171   13
%e A375171   31
%e A375171 -> 11 (1 time), 13 (1 time), 31 (1 time), 113 (1 time), 131 (1 time) are all reversible primes.
%e A375171 Table begins (upper left corner = T(1,1)):
%e A375171      2       37          337             3257 ...
%e A375171     37     1111       113131         11933371 ...
%e A375171    337   111331    113101311     119310213191 ...
%e A375171   3257 13139731 113101929311 1193100990013911 ...
%e A375171    ...      ...          ...              ... ...
%o A375171 (PARI)
%o A375171 isp(x) = ispseudoprime(x) && ispseudoprime(fromdigits(Vecrev(digits((x)))));
%o A375171 ispd(x) = ispseudoprime(fromdigits(x)) && ispseudoprime(fromdigits(Vecrev(x)));
%o A375171 vp(n) = select(isp, [10^(n-1)..10^n-1]);
%o A375171 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);
%o A375171 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
%Y A375171 Cf. A007500, A048054, A177513, A224164, A375234.
%K A375171 tabl,base,nonn
%O A375171 1,1
%A A375171 _Jean-Marc Rebert_, Aug 06 2024