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%I #19 Feb 28 2024 10:48:45
%S 1,1,1,1,1,2,2,1,1,1,2,2,1,1,1,1,1,1,1,2,2,2,1,1,2,2,2,2,1,3,2,3,1,1,
%T 2,1,2,2,1,2,1,2,2,1,3,3,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,2,3,2,2,2,3,
%U 1,1,1,2,2,3,2,1,1,2,1,1,2,1,1,1,1,1,1,1,1,1,1,2,1,2,1,1,1,1,1,1,1,1,1,1,2
%N Number of distinct primes obtained by cyclically shifting the decimal digits of the n-th prime.
%C First occurrence of k, k=1,2,3,...: 2, 13, 113, 1193, 11939, 193939, 17773937, 119139133, ..., . A247153.
%C a(n) is equal to the row index of prime(n) in A317716.
%C Every positive integer occurs in this sequence if and only if A247153(i) != 0 for every i >= 1.
%H Robert Israel, <a href="/A317756/b317756.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A262988(A000040(n)).
%t f[n_] := Block[{len = IntegerLength@n, s = {n}}, Do[AppendTo[s, FromDigits@RotateRight@IntegerDigits@s[[k - 1]]], {k, 2, len}]; DeleteDuplicates@Select[s, PrimeQ]] (* after Michael De Vlieger in A262988 *); Array[Length@f@Prime@# &, 105] (* _Robert G. Wilson v_, Aug 06 2018 *)
%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 a(n) = my(p=prime(n)); count_primes(p) \\ _Felix Fröhlich_, Aug 06 2018
%Y Cf. A000040, A262988, A247153, A317716.
%K base,easy,nonn
%O 1,6
%A _Felix Fröhlich_ and _Robert G. Wilson v_, Aug 06 2018
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