A190222 Noncomposite numbers all of whose decimal digits are noncomposite numbers (1,2,3,5,7).

1, 2, 3, 5, 7, 11, 13, 17, 23, 31, 37, 53, 71, 73, 113, 127, 131, 137, 151, 157, 173, 211, 223, 227, 233, 251, 257, 271, 277, 311, 313, 317, 331, 337, 353, 373, 521, 523, 557, 571, 577, 727, 733, 751, 757, 773, 1117, 1123, 1151, 1153, 1171, 1213, 1217, 1223

Offset: 1

Author

Jaroslav Krizek, May 06 2011

Keywords

• nonn
• base

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Chris Caldwell, The Prime Glossary, Unholey prime

Crossrefs

Subsequence of A001742.

Programs

Magma

[1] cat [n: n in PrimesUpTo(1223) | Set(Intseq(n)) subset [1, 2, 3, 5, 7]]; // Arkadiusz Wesolowski, Apr 16 2014

Mathematica

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

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

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

Formula

a(n) >> n^k where k = log(10)/log(5) = 1.43067.... - Charles R Greathouse IV, Dec 28 2017