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