|
Search: id:A107845
|
|
|
| A107845 |
|
Transposable-digit primes: Primes such that if any single pair of adjacent digits is transposed the result is a prime. |
|
+0
3
|
|
| 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, 97, 113, 131, 137, 179, 199, 277, 311, 331, 337, 373, 379, 397, 419, 491, 577, 613, 733, 811, 877, 911, 919, 977, 991, 1013, 1031, 1091, 1117, 1213, 1231, 1579, 1777, 1811, 1999, 2113, 2131, 2399, 2411, 2677, 2699, 2719
(list; graph; listen)
|
|
|
OFFSET
|
0,1
|
|
|
COMMENT
|
A single transposition error (of decimal digits) when recording or communicating such a prime still results in a prime (possibly the same prime). A003459 and A004022 (its subsequence) are subsequences. A003459 is also a subsequence of A068652.
|
|
EXAMPLE
|
137 is a term because it is prime and 173 and 317 are also prime.
173 is not a term because 713 is not prime (even though 173 and 137 are prime). {Hence none of 137,173,317,371,713,731 is a term of A003459}.
3119 is a term because it is prime and 1319 and 3191 are primes.
As 3119, 1193, 1931 and 9311 are all prime, 3119 is also a term of A068652.
Finally, although 1913 is also prime, neither 1139, 1391, 3911, 9113, nor 9131 is prime so 3119's twelve total permutations are not terms of A003459.
|
|
CROSSREFS
|
Cf. A003459 (absolute primes), A004022 (repunit primes), A068652 (every cyclic permutation is prime).
Sequence in context: A069706 A007500 A090933 this_sequence A090934 A068652 A003459
Adjacent sequences: A107842 A107843 A107844 this_sequence A107846 A107847 A107848
|
|
KEYWORD
|
base,nonn
|
|
AUTHOR
|
Rick L. Shepherd (rshepherd2(AT)hotmail.com), May 24 2005
|
|
|
Search completed in 0.002 seconds
|
