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

2,1

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

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

Sequence in context: A126534 A361915 A340844 * A089569 A048383 A230377

Adjacent sequences: A127824 A127825 A127826 * A127828 A127829 A127830

Keyword

nonn,base

Author

Ray Chandler, Jan 31 2007

Extensions

More terms from Robert Israel, Nov 19 2017

Status

approved