|
| |
|
|
A068679
|
|
Numbers which yield a prime whenever a 1 is inserted anywhere in them (including at the beginning or end).
|
|
17
|
|
|
|
1, 3, 7, 13, 31, 49, 63, 81, 91, 99, 103, 109, 117, 123, 151, 181, 193, 213, 231, 279, 319, 367, 427, 459, 571, 601, 613, 621, 697, 721, 801, 811, 951, 987, 1113, 1117, 1131, 1261, 1821, 1831, 1939, 2101, 2149, 2211, 2517, 2611, 3151, 3219, 4011, 4411, 4519, 4887, 5031, 5361, 6231, 6487, 6871, 7011, 7209, 8671, 9141, 9801, 10051
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
If R(p) = (10^p -1)/9 is a prime then {(10^(p-1) -1}/9 belongs to this sequence.
|
|
|
LINKS
|
Giovanni Resta, Table of n, a(n) for n = 1..3314 (terms < 2*10^13, first 1929 terms from Chai Wah Wu)
C. Caldwell, Prime Pages
|
|
|
EXAMPLE
|
123 belongs to this sequence as the numbers 1123, 1213, 1231 obtained by inserting a 1 in all possible ways are all primes.
|
|
|
MATHEMATICA
|
d[n_]:=IntegerDigits[n]; ins[n_]:=FromDigits/@Table[Insert[d[n], 1, k], {k, Length[d[n]]+1}]; Select[Range[10060], And@@PrimeQ/@ins[#] &] (* Jayanta Basu, May 20 2013 *)
Select[Range[11000], AllTrue[FromDigits/@Table[Insert[ IntegerDigits[ #], 1, n], {n, IntegerLength[#]+1}], PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 16 2020 *)
|
|
|
PROG
|
(Python)
from sympy import isprime
A068679_list, n = [], 1
while len(A068679_list) < 1000:
if isprime(10*n+1):
s = str(n)
for i in range(len(s)):
if not isprime(int(s[:i]+'1'+s[i:])):
break
else:
A068679_list.append(n)
n += 1 # Chai Wah Wu, Oct 02 2019
|
|
|
CROSSREFS
|
Cf. A068673, A068674, A068677, A069246.
Sequence in context: A163418 A309738 A161218 * A006978 A060424 A119962
Adjacent sequences: A068676 A068677 A068678 * A068680 A068681 A068682
|
|
|
KEYWORD
|
base,nonn
|
|
|
AUTHOR
|
Amarnath Murthy, Mar 02 2002
|
|
|
EXTENSIONS
|
More terms from Eli McGowan (ejmcgowa(AT)mail.lakeheadu.ca), Apr 11 2002
More terms from Vladeta Jovovic, Apr 16 2002
|
|
|
STATUS
|
approved
|
| |
|
|
