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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
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
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.)