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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. 1
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS 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: A107932 A143365 A090137 * A205707 A136491 A268487 Adjacent sequences:  A306923 A306924 A306925 * A306927 A306928 A306929 KEYWORD nonn,tabl,base AUTHOR Felix FrÃ¶hlich, Mar 16 2019 STATUS approved

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Last modified January 19 20:41 EST 2020. Contains 331066 sequences. (Running on oeis4.)