A127746
Smallest n-digit prime whose reversal is also prime.
Original entry on oeis.org
2, 13, 107, 1009, 10007, 100049, 1000033, 10000169, 100000007, 1000000007, 10000000207, 100000000237, 1000000000091, 10000000000313, 100000000000261, 1000000000000273, 10000000000000079, 100000000000000049
Offset: 1
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f[n_] := Block[{k = 10^(n - 1), id, rid}, While[ id = IntegerDigits[k]; rid = Reverse[id]; ! PrimeQ[k] || ! PrimeQ[FromDigits[rid]] || id == rid, k++ ]; k]; Table[f[n], {n, 2, 19}] (* Ray Chandler, Jan 30 2007 *)
sndp[n_]:=Module[{np=NextPrime[10^(n+1)]},While[PalindromeQ[np] || !PrimeQ[ IntegerReverse[ np]],np= NextPrime[np]];np]; Join[{2},Array[sndp,20,0]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 11 2017 *)
A127827
Smallest n-digit emirp (A006567) with nondecreasing digits.
Original entry on oeis.org
13, 113, 1223, 11149, 111119, 1111339, 11111117, 111111199, 1111111999, 11111111113, 111111111149, 1111111111267, 11111111111257, 111111111113447, 1111111111112227, 11111111111122223, 111111111111113569, 1111111111111113779, 11111111111111133677, 111111111111111111157, 1111111111111111122359, 11111111111111111133469
Offset: 2
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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
-
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
Showing 1-2 of 2 results.
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