A127827 Smallest n-digit emirp (A006567) with nondecreasing digits.

13, 113, 1223, 11149, 111119, 1111339, 11111117, 111111199, 1111111999, 11111111113, 111111111149, 1111111111267, 11111111111257, 111111111113447, 1111111111112227, 11111111111122223, 111111111111113569, 1111111111111113779, 11111111111111133677, 111111111111111111157, 1111111111111111122359, 11111111111111111133469

Offset: 2

Author

Ray Chandler, Jan 31 2007

Keywords

• nonn
• base

Links

• Michael S. Branicky, Table of n, a(n) for n = 2..529 (terms 2..225 from Robert Israel)

Crossrefs

Cf. A006567, A031991, A114018, A127747, A127828.

Programs

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

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

Extensions

More terms from Robert Israel, Nov 19 2017