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

1,1

Comments

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

Disjoint union of A124666 and (intersection of A065502 and A032352). - Reinhard Zumkeller, Oct 22 2011; edited by Michel Marcus, Aug 02 2022

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

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A010051, A032737, A125268.

Cf. A032352, A065502.

Cf. A124666.

Sequence in context: A032352 A333729 A183048 * A134989 A119873 A364307

Adjacent sequences: A124662 A124663 A124664 * A124666 A124667 A124668

Keyword

base,nonn

Author

Tanya Khovanova, Dec 23 2006

Extensions

Deleted incorrect Haskell program. - N. J. A. Sloane, Aug 02 2022

Status

approved