cp's OEIS Frontend

A344629 Primes p such that exactly five numbers among all circular permutations of the digits of p are prime.

%I A344629 #11 Jun 30 2021 09:04:28
%S A344629 11939,19391,19937,37199,39119,71993,91193,93719,93911,99371,103391,
%T A344629 103997,107119,110339,111893,111919,113123,113177,113983,114997,
%U A344629 117133,117319,117353,117701,118931,119107,119179,119191,119699,123113,127733,129919,131231,131771
%N A344629 Primes p such that exactly five numbers among all circular permutations of the digits of p are prime.
%H A344629 Felix Fröhlich, <a href="/A344629/b344629.txt">Table of n, a(n) for n = 1..10000</a>
%o A344629 (PARI) 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 A344629 eva(n) = subst(Pol(n), x, 10)
%o A344629 is(n) = my(r=rot(digits(n)), i=0); while(r!=digits(n), if(ispseudoprime(eva(r)), i++); r=rot(r)); if(ispseudoprime(eva(r)), i++); if(n==1 || n==11, return(0)); if(i==5, 1, 0)
%o A344629 forprime(p=1, 1e3, if(is(p), print1(p, ", ")))
%Y A344629 Cf. A270083. Row 5 of A317716.
%Y A344629 Cf. primes where exactly k numbers among all circular permutations of digits are prime: A068654 (k=1), A344626 (k=2), A344627 (k=3), A344628 (k=4), A344630 (k=6), A344631 (k=7), A344632 (k=8).
%K A344629 nonn,base
%O A344629 1,1
%A A344629 _Felix Fröhlich_, May 25 2021