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A306926 A(n, k) is the k-th prime p > 10 where a string of exactly n zeros can be inserted somewhere into the decimal expansion such that the resulting number is also prime; square array, read by antidiagonals, downwards.

%I A306926 #18 May 15 2019 02:58:06
%S A306926 11,13,19,17,23,17,19,31,19,13,37,41,71,23,13,41,43,73,29,23,23,53,47,
%T A306926 79,37,73,31,17,59,53,97,59,79,43,37,17,61,59,103,71,89,107,53,19,31,
%U A306926 67,67,149,97,179,127,59,47,43,13,71,71,151,103,223,131,61,61
%N A306926 A(n, k) is the k-th prime p > 10 where a string of exactly n zeros can be inserted somewhere into the decimal expansion such that the resulting number is also prime; square array, read by antidiagonals, downwards.
%e A306926 Array starts as follows:
%e A306926    11,  13,  17,  19,  37,  41,  53,  59,  61,  67,  71,  79,  89,  97
%e A306926    19,  23,  31,  41,  43,  47,  53,  59,  67,  71,  89,  97, 107, 109
%e A306926    17,  19,  71,  73,  79,  97, 103, 149, 151, 157, 173, 181, 223, 229
%e A306926    13,  23,  29,  37,  59,  71,  97, 103, 127, 137, 139, 157, 181, 199
%e A306926    13,  23,  73,  79,  89, 179, 223, 233, 239, 241, 263, 269, 277, 281
%e A306926    23,  31,  43, 107, 127, 131, 137, 139, 149, 151, 163, 173, 179, 181
%e A306926    17,  37,  53,  59,  61,  67,  71, 107, 109, 151, 179, 193, 197, 211
%e A306926    17,  19,  47,  61,  67,  71, 157, 181, 197, 227, 313, 347, 353, 367
%e A306926    31,  43, 103, 113, 127, 137, 149, 157, 163, 173, 191, 241, 257, 277
%e A306926    13,  79, 113, 139, 163, 191, 293, 313, 349, 397, 433, 439, 443, 449
%e A306926    23,  79,  89, 137, 149, 151, 163, 181, 199, 229, 239, 241, 277, 311
%e A306926    41,  79, 131, 157, 167, 197, 199, 227, 229, 233, 241, 347, 349, 359
%e A306926   137, 167, 191, 197, 227, 277, 281, 313, 337, 353, 389, 421, 439, 449
%e A306926 Antidiagonals as a triangular array:
%e A306926   11
%e A306926   13, 19
%e A306926   17, 23,  17
%e A306926   19, 31,  19,  13
%e A306926   37, 41,  71,  23,  13
%e A306926   41, 43,  73,  29,  23,  23
%e A306926   53, 47,  79,  37,  73,  31, 17
%e A306926   59, 53,  97,  59,  79,  43, 37, 17
%e A306926   61, 59, 103,  71,  89, 107, 53, 19,  31
%e A306926   67, 67, 149,  97, 179, 127, 59, 47,  43, 13
%e A306926   71, 71, 151, 103, 223, 131, 61, 61, 103, 79, 23
%o A306926 (PARI) insert(n, len, pos) = my(d=digits(n), v=[], w=[]); for(y=1, pos, v=concat(v, d[y])); v=concat(v, vector(len)); for(z=pos+1, #d, v=concat(v, d[z])); subst(Pol(v), x, 10)
%o A306926 row(n, terms) = my(i=0); if(terms <= 0, print1(""), forprime(p=10, , for(k=1, #digits(p)-1, my(zins=insert(p, n, k)); if(ispseudoprime(zins), print1(p, ", "); i++; break)); if(i>=terms, print(""); break)))
%o A306926 array(rows, cols) = for(x=1, rows-1, row(x, cols))
%o A306926 array(12, 10) \\ Print initial 12 rows and 10 columns of array
%Y A306926 Cf. A215417, A306920. Row 1 is A164329.
%K A306926 nonn,tabl,base
%O A306926 1,1
%A A306926 _Felix Fröhlich_, Mar 16 2019