A317716 Square array A(n, k), read by antidiagonals downwards: k-th prime p such that cyclic digit shifts produce exactly n different primes.

2, 3, 13, 5, 17, 113, 7, 31, 131, 1193, 11, 37, 197, 1931, 11939, 19, 71, 199, 3119, 19391, 193939, 23, 73, 311, 3779, 19937, 199933, 17773937, 29, 79, 337, 7793, 37199, 319993, 39371777, 119139133, 41, 97, 373, 7937, 39119, 331999, 71777393, 133119139

Offset

1,1

Comments

k-th prime p such that A262988(p) = n.

Are all rows of the array infinite?

A term q of A270083 occurs in row A055642(q) - 1 in this array.

A term r of A293663 occurs in row A055642(r) in this array.

Row 1 is a supersequence of A004022.

Column 1 is A247153.

Links

Robert G. Wilson v, Antidiagonals n = 1..13, flattened

Example

Array starts
          2,         3,         5,         7,        11,        19,        23, ...
         13,        17,        31,        37,        71,        73,        79, ...
        113,       131,       197,       199,       311,       337,       373, ...
       1193,      1931,      3119,      3779,      7793,      7937,      9311, ...
      11939,     19391,     19937,     37199,     39119,     71993,     91193, ...
     193939,    199933,    319993,    331999,    391939,    393919,    919393, ...
   17773937,  39371777,  71777393,  73937177,  77393717,  77739371,  93717773, ...
  119139133, 133119139, 139133119, 191391331, 311913913, 331191391, 913311913, ...
...

Prog

(PARI) eva(n) = subst(Pol(n), x, 10)
rot(n) = if(#Str(n)==1, v=vector(1), v=vector(#n-1)); for(i=2, #n, v[i-1]=n[i]); u=vector(#n); for(i=1, #n, u[i]=n[i]); v=concat(v, u[1]); v
count_primes(n) = my(d=digits(n), i=0); while(1, if(ispseudoprime(eva(d)), i++); d=rot(d); if(d==digits(n), return(i)))
row(n, terms) = my(i=0); forprime(p=1, , if(count_primes(p)==n, print1(p, ", "); i++); if(i==terms, print(""); break))
array(rows, cols) = for(x=1, rows, row(x, cols))
array(7, 7) \\ print initial 7 rows and 7 columns of array

Crossrefs

Cf. A004022, A055642, A247153, A262988, A270083, A293663.

Sequence in context: A085400 A067523 A035515 * A076988 A128369 A087568

Adjacent sequences: A317713 A317714 A317715 * A317717 A317718 A317719

Keyword

nonn,base,tabl

Author

Felix Fröhlich, Aug 05 2018

Status

approved