A124666 Numbers ending in 1, 3, 7 or 9 such that either prepending or following them by one digit doesn't produce a prime.

891, 921, 1029, 1037, 1653, 1763, 1857, 2427, 2513, 2519, 2607, 3111, 3193, 3213, 3501, 3519, 3707, 3953, 4227, 4459, 4599, 4689, 4803, 4863, 5019, 5043, 5047, 5397, 5459, 5489, 5499, 6019, 6023, 6429, 6483, 6609, 6621, 7113

Offset: 1

Author

Tanya Khovanova, Dec 23 2006

Keywords

• base
• nonn

Comments

If the number doesn't end in 1, 3, 7 or 9, then the prepending requirement is automatically satisfied. Hence it becomes nonrestrictive and not very interesting.

Examples

			The definition means that 891, 1891, 2891, 3891, 4891, 5891, 6891, 7891, 8891, 9891, 8911, 8913, 8917 and 8919 are all composite numbers.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..4000

Crossrefs

Cf. A124665.

Programs

Mathematica

dppQ[n_]:=AllTrue[Join[{n},Table[m*10^IntegerLength[n]+n,{m,9}],Table[ n*10+k,{k,{1,3,7,9}}]],CompositeQ]; Select[Range[8000],MemberQ[ {1,3,7,9},Mod[ #,10]]&&dppQ[#]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 19 2018 *)

Python

from sympy import isprime
def ok(n):
    s = str(n)
    if s[-1] not in "1379": return False
    if any(isprime(int(s+c)) for c in "1379"): return False
    return not any(isprime(int(c+s)) for c in "0123456789")
print([k for k in range(7114) if ok(k)]) # Michael S. Branicky, Aug 02 2022