|
Search: id:A072857
|
|
|
| A072857 |
|
Primeval numbers: numbers that set a record for the number of distinct primes that can be obtained by permuting some subset of their digits. |
|
+0
8
|
|
| 1, 2, 13, 37, 107, 113, 137, 1013, 1037, 1079, 1237, 1367, 1379, 10079, 10123, 10136, 10139, 10237, 10279, 10367, 10379, 12379, 13679, 100279, 100379, 101237, 102347, 102379, 103679, 123479, 1001237, 1002347, 1002379, 1003679, 1012349, 1012379
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
RECORDS transform of A075053. [I think this comment is wrong. The sequence is really the RECORDS transform of A039993. - njas, Jan 25 2008.]
"73 is the largest integer with the property that all permutations of all of its substrings are primes." M. Keith.
Smallest monotonic increasing subsequence of A076449. - Lekraj Beedassy (blekraj(AT)yahoo.com), Sep 23 2006
|
|
REFERENCES
|
J.-P. Delahaye, Merveilleux nombres premiers ("Amazing primes"), "1379's quite primeval, is it not?", pp. 318-321, Pour la Science, Paris 2000.
|
|
LINKS
|
C. K. Caldwell, The Prime Glossary, primeval number
J. P. Delahaye, Primes Hunters, 1379 is very primeval (in French)
M. Keith, Integers Containing Many Embedded Primes
W. Schneider, Primeval Numbers
N. J. A. Sloane, Transforms
G. Villemin's Almanach of Numbers, Mike Keith's Primeval Number
Wikipedia, Primeval number
|
|
EXAMPLE
|
1379 is in the sequence because it is the smallest number whose digital permutations form a total of 31 primes, viz. 3, 7, 13, 17, 19, 31, 37, 71, 73, 79, 97, 137, 139, 173, 179, 193, 197, 317, 379, 397, 719, 739, 937, 971, 1973, 3719, 3917, 7193, 9137, 9173, 9371.
|
|
MATHEMATICA
|
(*first do *) Needs["DiscreteMath`Combinatorica`"] (* then *) f[n_] := Length[ Select[ FromDigits /@ Flatten[ Permutations /@ Subsets[ IntegerDigits[ n]], 1], PrimeQ[ # ] &]]; d = -1; Do[ b = f[n]; If[b > d, Print[n]; d = b], {n, 2^20}] (from Robert G. Wilson v Feb 12 2005)
|
|
CROSSREFS
|
Cf. A039993, A075053, A076497. A076449 gives a similar sequence.
Cf. A119535 (prime subsequence).
Sequence in context: A034011 A085497 A005113 this_sequence A119535 A011919 A042795
Adjacent sequences: A072854 A072855 A072856 this_sequence A072858 A072859 A072860
|
|
KEYWORD
|
base,nonn
|
|
AUTHOR
|
Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 26 2002
|
|
EXTENSIONS
|
Edited, corrected and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 12 2002
|
|
|
Search completed in 0.002 seconds
|
