A091898 - OEIS

%I #2 Mar 30 2012 17:36:41

%S 14,16,19,20,23,29,30,32,34,35,38,41,43,47,50,53,59,61,67,70,74,76,83,

%T 89,91,92,95,98,101,103,104,106,107,109,110,112,115,118,119,121,124,

%U 125,127,128,130,133,134,136,137,139,140,142,143,145,146,149,151,152,154

%N Numbers that change from composite to prime or vice versa for at least one permutation of their digits.

%C This is actually a subsequence of the complement of A091897, the union of A003459 and A067012: This sequence contains no powers of 10 (A011557) as 1 is not prime.

%C Clearly also no repdigit number (A010785) is a term nor is any number with only even digits (except for 20,200,2000,...) nor is any number divisible by 3 (except for 30,300,3000,...). Among other primes, this sequence does include all primes p > 5 which contain at least one of the digits 0,2,4,5,6,8.

%e 14=2*7 (composite) is a term as a permutation of its digits gives 41 (prime).

%e Hence 41 is also a term. 19 (prime) is a term as 91=7*13 (composite). Thus 91

%e is also a term. 130=2*5*13 (composite) is a term (even though the permutation

%e 310=2*5*31 is also composite) because another permutation (0)13 (prime) exists

%e (dropping the leading 0). 13, however, is not a term as 31 is also prime (13

%e and 31 are members of A003459).

%Y Cf. A003459 (absolute primes), A067012 ('absolute composites'), A091897 (union of A003459 and A067012), A010785 (repdigit numbers).

%K base,nonn

%O 1,1

%A _Rick L. Shepherd_, Feb 09 2004