The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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. 16
 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, 1023457, 1023467, 1023479, 1234579, 1234679, 10012349 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS RECORDS transform of A039993. - N. J. A. Sloane, Jan 25 2008. See A239196 and A239197 for the RECORDS transform of the closely related sequence A075053. - M. F. Hasler, Mar 12 2014 "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, Sep 23 2006 From M. F. Hasler, Oct 15 2019: All terms > 37 start with leading digit 1 and have all other digits in nondecreasing order. The terms are smallest representatives of the class of numbers having the same digits, cf. A179239 and A328447 which both contain this as a subsequence. The frequency of primes is roughly 50% for the displayed values, but appears to decrease. Can it be proved that the asymptotic density is zero? Can we prove that there are infinitely many even terms? (Of the form 10...01..12345678?) Can it be proved that there is no term that is a multiple of 3? (Or the contrary? Are there infinitely many?) (End) 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 Giovanni Resta, Table of n, a(n) for n = 1..100 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, Nombre Primeval de Mike Keith 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}] (* Robert G. Wilson v, Feb 12 2005 *) PROG (PARI) A072857_upto(num_digits, s=1, m=-1, L=List())={for(n=s, num_digits, my(u=10^(n-1)); forvec(v=vector(n-(n>2), i, [0, if(n>6, 9*(i+1)\n, n>3, 10-(n-i)\.6, 7)]), m

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 10 05:56 EDT 2024. Contains 375044 sequences. (Running on oeis4.)