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A211685 Prime numbers > 1000 such that all the substrings of length >= 3 are primes (substrings with leading '0' are considered to be nonprime). 49
1277, 1373, 1499, 1571, 1733, 1811, 1997, 2113, 2239, 2293, 2719, 3137, 3313, 3373, 3491, 3499, 3593, 3673, 3677, 3733, 3739, 3797, 4211, 4337, 4397, 4673, 4877, 4919, 5233, 5419, 5479, 6131, 6173, 6197, 6199, 6311, 6317, 6599, 6619, 6733 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Only numbers > 1000 are considered, since all 3-digit primes are trivial members.
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.
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.
LINKS
Hieronymus Fischer, Table of n, a(n) for n = 1..63 (complete sequence).
EXAMPLE
a(1)=1277, since all substrings of length >= 3 are primes (127, 277, and 1277).
a(63)=349199, all substrings of length >= 3 (349, 491, 919, 199, 3491, 4919, 9199, 34919, 49199 and 349199) are primes.
CROSSREFS
Sequence in context: A318201 A236013 A282440 * A210365 A190831 A202643
KEYWORD
nonn,fini,base,full
AUTHOR
Hieronymus Fischer, Jun 08 2012
STATUS
approved

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Last modified April 21 13:26 EDT 2024. Contains 371870 sequences. (Running on oeis4.)