A091633 Primes having only {1, 3, 7, 9} as digits.

3, 7, 11, 13, 17, 19, 31, 37, 71, 73, 79, 97, 113, 131, 137, 139, 173, 179, 191, 193, 197, 199, 311, 313, 317, 331, 337, 373, 379, 397, 719, 733, 739, 773, 797, 911, 919, 937, 971, 977, 991, 997, 1117, 1171, 1193, 1319, 1373, 1399, 1733, 1777, 1913, 1931, 1933

Offset: 1

Author

Enoch Haga, Jan 26 2004

Keywords

• easy
• nonn
• base

Comments

Some primes of sufficient length might be termed DNA primes if the sequence of digits 1,3,7,9 in any order happens to be an appropriate analog of the DNA bases A, G, C, T. It would be interesting to know if it is possible for any DNA sequence to match a DNA prime.

Links

• Pierre Cami and Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 (first 5058 terms from Pierre Cami)
• Index to entries for primes with digits in a given set

Crossrefs

Subsequence of A136333, A245193, and A030096.

A091871 gives prime index.

Cf. A010051.

Programs

Haskell

a091633 n = a091633_list !! (n-1)
a091633_list = filter ((== 1) . a010051') a136333_list
-- Reinhard Zumkeller, Jul 17 2014

Mathematica

Select[Flatten[Table[FromDigits/@Tuples[{1,3,7,9},n],{n,4}]],PrimeQ] (* Harvey P. Dale, Jun 26 2015 *)

Formula

Select primes having digits 1, 3, 7, 9 only.

a(n) = A000040(A091871(n)). - R. J. Mathar, Aug 29 2018