A344630 - OEIS

%I #13 Sep 22 2024 12:51:19

%S 193939,199933,319993,331999,391939,393919,919393,933199,939193,

%T 939391,993319,999331,1313999,1317727,1399913,1731893,1743737,1772713,

%U 1893173,1977779,2713177,3139991,3173189,3177271,3189317,3717437,4373717,7174373,7271317,7318931

%N Primes p such that exactly six numbers among all circular permutations of the digits of p are prime.

%H Felix Fröhlich, <a href="/A344630/b344630.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Prime[Range[500000]],Total[Boole[PrimeQ[FromDigits/@Table[RotateRight[IntegerDigits[#],n],{n,0,IntegerLength[ #]-1}]]]]==6&] (* _Harvey P. Dale_, Sep 22 2024 *)

%o (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 eva(n) = subst(Pol(n), x, 10)

%o 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==6, 1, 0)

%o forprime(p=1, 1e3, if(is(p), print1(p, ", ")))

%Y Cf. A270083. Row 6 of A317716.

%Y 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), A344629 (k=5), A344631 (k=7), A344632 (k=8).

%K nonn,base,changed

%O 1,1

%A _Felix Fröhlich_, May 25 2021