A124665 - OEIS

%I #43 Jan 07 2023 02:00:04

%S 20,32,62,84,114,126,134,135,146,150,164,168,176,185,192,196,204,210,

%T 218,232,236,240,248,256,258,282,294,298,305,314,315,324,326,328,342,

%U 348,350,356,366,368,374,375,378,395,406,408,410,414,416,418

%N Numbers that cannot be either prefixed or followed by one digit to form a prime.

%C Prefixing by 0 gives the number itself, implying that a(n) is not prime.

%C Disjoint union of A124666 and (intersection of A065502 and A032352). - _Reinhard Zumkeller_, Oct 22 2011; edited by _Michel Marcus_, Aug 02 2022

%C All integers of the form 100*(21*n)^3 belong to the sequence, so it is infinite. - _Mauro Fiorentini_, Jan 05 2023

%H Michael S. Branicky, <a href="/A124665/b124665.txt">Table of n, a(n) for n = 1..10000</a>

%e If you prefix 20 with any digit you will get an even number. Also 201, 203, 207 and 209 are all composite.

%t okQ[n_]:=If[EvenQ[n]||Divisible[n,5],Union[PrimeQ[10 n+{1,3,7,9}]] == {False},!PrimeQ[n]&&Union[PrimeQ[10 n+{1,3,7,9}]]=={False} && Union[ PrimeQ[Table[FromDigits[Join[{i},IntegerDigits[n]]],{i,9}]]] == {False}]; Select[Range[500],okQ] (* _Harvey P. Dale_, Jul 15 2011 *)

%o (PARI) is(n)=my(N=10*n,D=10^#Str(n)); forstep(k=n, n+9*D, D, if(isprime(k), return(0)));!(isprime(N+1)||isprime(N+3)||isprime(N+7)||isprime(N+9)) \\ _Charles R Greathouse IV_, Jul 15 2011

%o (Python)

%o from sympy import isprime

%o def ok(n):

%o     s = str(n)

%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(419) if ok(k)]) # _Michael S. Branicky_, Aug 01 2022

%Y Cf. A010051, A032737, A125268.

%Y Cf. A032352, A065502.

%Y Cf. A124666.

%K base,nonn

%O 1,1

%A _Tanya Khovanova_, Dec 23 2006

%E Deleted incorrect Haskell program. - _N. J. A. Sloane_, Aug 02 2022