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A127827
Smallest n-digit emirp (A006567) with nondecreasing digits.
2
13, 113, 1223, 11149, 111119, 1111339, 11111117, 111111199, 1111111999, 11111111113, 111111111149, 1111111111267, 11111111111257, 111111111113447, 1111111111112227, 11111111111122223, 111111111111113569, 1111111111111113779, 11111111111111133677, 111111111111111111157, 1111111111111111122359, 11111111111111111133469
OFFSET
2,1
LINKS
Michael S. Branicky, Table of n, a(n) for n = 2..529 (terms 2..225 from Robert Israel)
MAPLE
nextl:= proc(L)
local m, k, r;
# L a list of digits 1-9, last odd, in nondecreasing order
if L[-1]<= 7 then return subsop(-1=L[-1]+2, L) fi;
m:= nops(L); k:= m-1;
while L[k] =9 do k:= k-1 od:
r:= [op(L[1..k-1]), (L[k]+1) $ (m+1-k)];
if r[-1]::even then r:= subsop(-1=r[-1]+1, r) fi;
r
end proc:
f:= proc(n) local L, p, q, i;
L:= [1$n];
do
p:= add(L[i]*10^(i-1), i=1..n);
q:= add(L[-i]*10^(i-1), i=1..n);
if q <> p and isprime(p) and isprime(q) then return(q) fi;
L:= nextl(L);
od
end proc:
map(f, [$2..30]); # Robert Israel, Nov 19 2017
PROG
(Python)
from sympy import isprime
from itertools import count, islice, combinations_with_replacement as mc
def bgen(d):
nd = ("".join(m) for m in mc("123456789", d))
yield from filter(isprime, map(int, nd))
def ok(ndp):
s = str(ndp)
return len(set(s)) != 1 and isprime(int(s[::-1]))
def agen():
yield from (next(filter(ok, bgen(d))) for d in count(2))
print(list(islice(agen(), 22))) # Michael S. Branicky, Jun 26 2022
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Ray Chandler, Jan 31 2007
EXTENSIONS
More terms from Robert Israel, Nov 19 2017
STATUS
approved