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

1,1

Links

Table of n, a(n) for n=1..63.

Example

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

Prog

(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

Crossrefs

Cf. A215417, A306920. Row 1 is A164329.

Sequence in context: A143365 A090137 A358573 * A205707 A136491 A357074

Adjacent sequences: A306923 A306924 A306925 * A306927 A306928 A306929

Keyword

nonn,tabl,base

Author

Felix Fröhlich, Mar 16 2019

Status

approved