A124665 Numbers that cannot be either prefixed or followed by one digit to form a prime.
20, 32, 62, 84, 114, 126, 134, 135, 146, 150, 164, 168, 176, 185, 192, 196, 204, 210, 218, 232, 236, 240, 248, 256, 258, 282, 294, 298, 305, 314, 315, 324, 326, 328, 342, 348, 350, 356, 366, 368, 374, 375, 378, 395, 406, 408, 410, 414, 416, 418
Offset: 1
Examples
If you prefix 20 with any digit you will get an even number. Also 201, 203, 207 and 209 are all composite.
Links
- Michael S. Branicky, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
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 *) -
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
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Python
from sympy import isprime def ok(n): s = str(n) 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(419) if ok(k)]) # Michael S. Branicky, Aug 01 2022
Extensions
Deleted incorrect Haskell program. - N. J. A. Sloane, Aug 02 2022
Comments