A083427 Smallest prime which is a concatenation of n distinct primes.

2, 23, 257, 2357, 112573, 11132357, 1113223537, 111317193257, 11131719223357, 1113171922335437, 111317192232934157, 11131719223293135773, 1113171922329313375759, 111317192232931337415743, 11131719223293133741435717

Offset

1,1

Links

Table of n, a(n) for n=1..15.

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