A190222 - OEIS

%I #20 Apr 03 2023 10:36:12

%S 1,2,3,5,7,11,13,17,23,31,37,53,71,73,113,127,131,137,151,157,173,211,

%T 223,227,233,251,257,271,277,311,313,317,331,337,353,373,521,523,557,

%U 571,577,727,733,751,757,773,1117,1123,1151,1153,1171,1213,1217,1223

%N Noncomposite numbers all of whose decimal digits are noncomposite numbers (1,2,3,5,7).

%H G. C. Greubel, <a href="/A190222/b190222.txt">Table of n, a(n) for n = 1..1000</a>

%H Chris Caldwell, The Prime Glossary, <a href="https://t5k.org/glossary/xpage/UnholeyPrime.html">Unholey prime</a>

%F a(n) >> n^k where k = log(10)/log(5) = 1.43067.... - _Charles R Greathouse IV_, Dec 28 2017

%t Join[{1}, Select[Range[2000], PrimeQ[#] && Intersection[{0, 4, 6, 8, 9}, IntegerDigits[#]] == {} &]] (* _T. D. Noe_, May 09 2011 *)

%o (Magma) [1] cat [n: n in PrimesUpTo(1223) | Set(Intseq(n)) subset [1, 2, 3, 5, 7]]; // _Arkadiusz Wesolowski_, Apr 16 2014

%o (PARI) is(k) = if(!isprime(k) && k != 1, return(0)); setminus(vecsort(digits(k), , 8), [1, 2, 3, 5, 7]) == [] \\ _Iain Fox_, Dec 28 2017

%o (PARI) is(n) = if(isprime(n), #setminus(Set(digits(k)), [1,2,3,5,7])==0, n==1) \\ _Charles R Greathouse IV_, Dec 28 2017

%Y Subsequence of A001742.

%K nonn,base

%O 1,2

%A _Jaroslav Krizek_, May 06 2011