A033274 - OEIS

%I #41 Jun 29 2022 13:40:29

%S 2,3,5,7,11,19,41,61,89,101,109,149,181,401,409,449,491,499,601,691,

%T 809,881,991,1009,1049,1069,1481,1609,1669,1699,1801,4001,4049,4481,

%U 4649,4801,4909,4969,6091,6469,6481,6869,6949,8009,8069,8081,8609,8669,8681

%N Primes that do not contain any other prime as a proper substring.

%C If there is more than one digit, all digits must be nonprime numbers.

%C A179335(n) = prime(n) iff prime(n) is in this sequence. For n > 4, prime(n) is in this sequence iff A109066(n) = 0. - _Reinhard Zumkeller_, Jul 11 2010, corrected by _M. F. Hasler_, Aug 27 2012

%C A079066(n) = 0 iff prime(n) is in this sequence. [Corrected by _M. F. Hasler_, Aug 27 2012]

%C What are the asymptotics of this sequence? - _Charles R Greathouse IV_, Aug 27 2012

%H Michael S. Branicky, <a href="/A033274/b033274.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Zak Seidov)

%e 149 is a term as 1, 4, 9, 14, 49 are all nonprimes.

%e 199 is not a term as 19 is a prime.

%t f[n_] := Block[ {id = IntegerDigits@n}, len = Length@ id - 1; Count[ PrimeQ@ Union[ FromDigits@# & /@ Flatten[ Table[ Partition[ id, k, 1], {k, len}], 1]], True] + 1]; Select[ Prime@ Range@ 1100, f@# == 1 &] (* _Robert G. Wilson v_, Aug 01 2010 *)

%o (Haskell)

%o import Data.List (elemIndices)

%o a033274 n = a033274_list !! (n-1)

%o a033274_list = map (a000040 . (+ 1)) $ elemIndices 0 a079066_list

%o -- _Reinhard Zumkeller_, Jul 19 2011

%o (Python)

%o from sympy import isprime

%o def ok(n):

%o     if n in {2, 3, 5, 7}: return True

%o     s = str(n)

%o     if set(s) & {"2", "3", "5", "7"} or not isprime(n): return False

%o     ss2 = set(s[i:i+l] for i in range(len(s)-1) for l in range(2, len(s)))

%o     return not any(isprime(int(ss)) for ss in ss2)

%o print([k for k in range(9000) if ok(k)]) # _Michael S. Branicky_, Jun 29 2022

%Y Cf. A089768, A089770, A039996, A079397, A033274, A034844, A179909-A179919.

%K base,nonn

%O 1,1

%A _Michael Kleber_

%E Edited by _N. J. A. Sloane_ at the suggestion of Luca Colucci, Apr 03 2008