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A317716
Square array A(n, k), read by antidiagonals downwards: k-th prime p such that cyclic digit shifts produce exactly n different primes.
10
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
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
KEYWORD
nonn,base,tabl
AUTHOR
Felix Fröhlich, Aug 05 2018
STATUS
approved