

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
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OFFSET

1,2


COMMENTS

If R(p) = (10^p 1)/9 is a prime then {(10^(p1) 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 *)


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



