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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 *) 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

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Last modified November 29 17:53 EST 2020. Contains 338769 sequences. (Running on oeis4.)