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%I #17 Aug 02 2022 09:21:10
%S 891,921,1029,1037,1653,1763,1857,2427,2513,2519,2607,3111,3193,3213,
%T 3501,3519,3707,3953,4227,4459,4599,4689,4803,4863,5019,5043,5047,
%U 5397,5459,5489,5499,6019,6023,6429,6483,6609,6621,7113
%N Numbers ending in 1, 3, 7 or 9 such that either prepending or following them by one digit doesn't produce a prime.
%C 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.
%H Harvey P. Dale, <a href="/A124666/b124666.txt">Table of n, a(n) for n = 1..4000</a>
%e The definition means that 891, 1891, 2891, 3891, 4891, 5891, 6891, 7891, 8891, 9891, 8911, 8913, 8917 and 8919 are all composite numbers.
%t 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 *)
%o (Python)
%o from sympy import isprime
%o def ok(n):
%o s = str(n)
%o if s[-1] not in "1379": return False
%o if any(isprime(int(s+c)) for c in "1379"): return False
%o return not any(isprime(int(c+s)) for c in "0123456789")
%o print([k for k in range(7114) if ok(k)]) # _Michael S. Branicky_, Aug 02 2022
%Y Cf. A124665.
%K base,nonn
%O 1,1
%A _Tanya Khovanova_, Dec 23 2006
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