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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. 3
 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 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

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Last modified June 15 03:12 EDT 2024. Contains 373402 sequences. (Running on oeis4.)