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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 *)

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

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Last modified December 14 19:27 EST 2019. Contains 329987 sequences. (Running on oeis4.)