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

1,1

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.

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A124665.

Sequence in context: A110726 A204366 A266915 * A125303 A087672 A284842

Adjacent sequences: A124663 A124664 A124665 * A124667 A124668 A124669

Keyword

base,nonn

Author

Tanya Khovanova, Dec 23 2006

Status

approved