OFFSET
1,1
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
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