A211685 - OEIS

%I #14 Jul 16 2015 22:13:00

%S 1277,1373,1499,1571,1733,1811,1997,2113,2239,2293,2719,3137,3313,

%T 3373,3491,3499,3593,3673,3677,3733,3739,3797,4211,4337,4397,4673,

%U 4877,4919,5233,5419,5479,6131,6173,6197,6199,6311,6317,6599,6619,6733

%N Prime numbers > 1000 such that all the substrings of length >= 3 are primes (substrings with leading '0' are considered to be nonprime).

%C Only numbers > 1000 are considered, since all 3-digit primes are trivial members.

%C By definition, each term of the sequence with more than 4 digits is built up by an overlapped union of previous terms, i.e., a(59)=33739 has the two embedded previous terms a(14)=3373 and a(21)=3739.

%C The sequence is finite, the last term is 349199 (n=63). Proof of finiteness: Let p be a number with more than 6 digits. By the argument above, each 6-digit substring of p must be a previous term. The only 6-digit term is 349199. Thus, there is no number p with the desired property.

%H Hieronymus Fischer, <a href="/A211685/b211685.txt">Table of n, a(n) for n = 1..63</a> (complete sequence).

%e a(1)=1277, since all substrings of length >= 3 are primes (127, 277, and 1277).

%e a(63)=349199, all substrings of length >= 3 (349, 491, 919, 199, 3491, 4919, 9199, 34919, 49199 and 349199) are primes.

%Y Cf. A019546, A035232, A039996, A046034, A069489, A085823, A211681, A211682, A211684.

%K nonn,fini,base,full

%O 1,1

%A _Hieronymus Fischer_, Jun 08 2012