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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.

%I A317716 #21 Aug 21 2018 03:44:44
%S A317716 2,3,13,5,17,113,7,31,131,1193,11,37,197,1931,11939,19,71,199,3119,
%T A317716 19391,193939,23,73,311,3779,19937,199933,17773937,29,79,337,7793,
%U A317716 37199,319993,39371777,119139133,41,97,373,7937,39119,331999,71777393,133119139
%N A317716 Square array A(n, k), read by antidiagonals downwards: k-th prime p such that cyclic digit shifts produce exactly n different primes.
%C A317716 k-th prime p such that A262988(p) = n.
%C A317716 Are all rows of the array infinite?
%C A317716 A term q of A270083 occurs in row A055642(q) - 1 in this array.
%C A317716 A term r of A293663 occurs in row A055642(r) in this array.
%C A317716 Row 1 is a supersequence of A004022.
%C A317716 Column 1 is A247153.
%H A317716 Robert G. Wilson v, <a href="/A317716/b317716.txt">Antidiagonals n = 1..13, flattened</a>
%e A317716 Array starts
%e A317716           2,         3,         5,         7,        11,        19,        23, ...
%e A317716          13,        17,        31,        37,        71,        73,        79, ...
%e A317716         113,       131,       197,       199,       311,       337,       373, ...
%e A317716        1193,      1931,      3119,      3779,      7793,      7937,      9311, ...
%e A317716       11939,     19391,     19937,     37199,     39119,     71993,     91193, ...
%e A317716      193939,    199933,    319993,    331999,    391939,    393919,    919393, ...
%e A317716    17773937,  39371777,  71777393,  73937177,  77393717,  77739371,  93717773, ...
%e A317716   119139133, 133119139, 139133119, 191391331, 311913913, 331191391, 913311913, ...
%e A317716 ...
%o A317716 (PARI) eva(n) = subst(Pol(n), x, 10)
%o A317716 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
%o A317716 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)))
%o A317716 row(n, terms) = my(i=0); forprime(p=1, , if(count_primes(p)==n, print1(p, ", "); i++); if(i==terms, print(""); break))
%o A317716 array(rows, cols) = for(x=1, rows, row(x, cols))
%o A317716 array(7, 7) \\ print initial 7 rows and 7 columns of array
%Y A317716 Cf. A004022, A055642, A247153, A262988, A270083, A293663.
%K A317716 nonn,base,tabl
%O A317716 1,1
%A A317716 _Felix Fröhlich_, Aug 05 2018