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.

11, 13, 19, 17, 23, 17, 19, 31, 19, 13, 37, 41, 71, 23, 13, 41, 43, 73, 29, 23, 23, 53, 47, 79, 37, 73, 31, 17, 59, 53, 97, 59, 79, 43, 37, 17, 61, 59, 103, 71, 89, 107, 53, 19, 31, 67, 67, 149, 97, 179, 127, 59, 47, 43, 13, 71, 71, 151, 103, 223, 131, 61, 61

Offset: 1

Author

Felix Fröhlich, Mar 16 2019

Keywords

• nonn
• tabl
• base

Examples

			Array starts as follows:
   11,  13,  17,  19,  37,  41,  53,  59,  61,  67,  71,  79,  89,  97
   19,  23,  31,  41,  43,  47,  53,  59,  67,  71,  89,  97, 107, 109
   17,  19,  71,  73,  79,  97, 103, 149, 151, 157, 173, 181, 223, 229
   13,  23,  29,  37,  59,  71,  97, 103, 127, 137, 139, 157, 181, 199
   13,  23,  73,  79,  89, 179, 223, 233, 239, 241, 263, 269, 277, 281
   23,  31,  43, 107, 127, 131, 137, 139, 149, 151, 163, 173, 179, 181
   17,  37,  53,  59,  61,  67,  71, 107, 109, 151, 179, 193, 197, 211
   17,  19,  47,  61,  67,  71, 157, 181, 197, 227, 313, 347, 353, 367
   31,  43, 103, 113, 127, 137, 149, 157, 163, 173, 191, 241, 257, 277
   13,  79, 113, 139, 163, 191, 293, 313, 349, 397, 433, 439, 443, 449
   23,  79,  89, 137, 149, 151, 163, 181, 199, 229, 239, 241, 277, 311
   41,  79, 131, 157, 167, 197, 199, 227, 229, 233, 241, 347, 349, 359
  137, 167, 191, 197, 227, 277, 281, 313, 337, 353, 389, 421, 439, 449
Antidiagonals as a triangular array:
  11
  13, 19
  17, 23,  17
  19, 31,  19,  13
  37, 41,  71,  23,  13
  41, 43,  73,  29,  23,  23
  53, 47,  79,  37,  73,  31, 17
  59, 53,  97,  59,  79,  43, 37, 17
  61, 59, 103,  71,  89, 107, 53, 19,  31
  67, 67, 149,  97, 179, 127, 59, 47,  43, 13
  71, 71, 151, 103, 223, 131, 61, 61, 103, 79, 23
		

Crossrefs

Cf. A215417, A306920. Row 1 is A164329.

Programs

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)
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)))
array(rows, cols) = for(x=1, rows-1, row(x, cols))
array(12, 10) \\ Print initial 12 rows and 10 columns of array