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 A083427 Smallest prime which is a concatenation of n distinct primes. 3
 2, 23, 257, 2357, 112573, 11132357, 1113223537, 111317193257, 11131719223357, 1113171922335437, 111317192232934157, 11131719223293135773, 1113171922329313375759, 111317192232931337415743, 11131719223293133741435717 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS EXAMPLE a(5) = 112573 is a concatenation of 11,2,5,7 and 3 and is the smallest such prime. a(7) <= 1113223537 = 11//13//2//23//5//3//7. - R. J. Mathar, Mar 19 2011 a(8) <= 111317193257 = 11//13//17//19//3//2//5//7. - Jonathan Vos Post, Mar 20 2006 a(9) <= 11131719223357 = 11//13//17//19//2//23//3//5//7. - R. J. Mathar, Mar 19 2011 PROG (Sage) concat = lambda x: Integer(''.join(str(i) for i in x), base=10) def A083427(n):     def primelists(sofar, widths):         if not widths: yield sofar; return         w = widths[0]         for p in prime_range(10**(w-1), 10**w):             if p not in sofar:                 for pv in primelists(sofar+[p], widths[1:]):                     yield pv     for numdig in PositiveIntegers():         least = None         for part in Partitions(numdig, length=n):             if list(part).count(1) > 4: continue # optimization             for sizes in Permutations(part):                 for plist in primelists([], sizes):                     x = concat(plist)                     if is_prime(x): least = min(x, least) if least else x                     # since x is increasing in this inner loop,                     # no need to continue if we can't improve                     if least and x >= least: break         if least: return least # D. S. McNeil, Mar 20 2011 CROSSREFS Cf. A000040. Sequence in context: A233783 A300326 A068983 * A083470 A064110 A176936 Adjacent sequences:  A083424 A083425 A083426 * A083428 A083429 A083430 KEYWORD base,more,nonn AUTHOR Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Apr 29 2003 EXTENSIONS a(7), a(8) from Jonathan Vos Post, Mar 20 2006 a(7) corrected by Emmanuel Vantieghem, Mar 19 2011 a(8) deleted on grounds that it is quite likely to be wrong. - N. J. A. Sloane, Mar 19 2011 a(7)-a(15) from D. S. McNeil, Mar 20 2011 STATUS approved

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Last modified June 20 12:34 EDT 2021. Contains 345164 sequences. (Running on oeis4.)