A032352 Numbers k such that there is no prime between 10*k and 10*k+9.

20, 32, 51, 53, 62, 84, 89, 107, 113, 114, 126, 133, 134, 135, 141, 146, 150, 164, 167, 168, 171, 176, 179, 185, 189, 192, 196, 204, 207, 210, 218, 219, 232, 236, 240, 248, 249, 251, 256, 258, 282, 294, 298, 305, 309, 314, 315, 317, 323, 324, 326, 328, 342

Offset: 1

Author

Jeff Burch

Keywords

• nonn
• base
• easy

Comments

Numbers k with property that appending any single decimal digit to k does not produce a prime.

A007920(n*10) > 10.

Examples

			m=32: 321=3*107, 323=17*19, 325=5*5*13, 327=3*109, 329=7*47, therefore 32 is a term.
		

Links

• M. I. Wilczynski, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A124665 (subsequence), A010051, A007811, A216292, A216293.

Programs

Haskell

a032352 n = a032352_list !! (n-1)
a032352_list = filter
   (\x -> all (== 0) $ map (a010051 . (10*x +)) [1..9]) [1..]
-- Reinhard Zumkeller, Oct 22 2011

Magma

[n: n in [1..350] | IsZero(#PrimesInInterval(10*n, 10*n+9))]; // Bruno Berselli, Sep 04 2012

Maple

a:=proc(n) if map(isprime,{seq(10*n+j,j=1..9)})={false} then n else fi end: seq(a(n),n=1..350); # Emeric Deutsch, Aug 01 2005

Mathematica

f[n_] := PrimePi[10n + 10] - PrimePi[10n]; Select[ Range[342], f[ # ] == 0 &] (* Robert G. Wilson v, Sep 24 2004 *)
Select[Range[342], NextPrime[10 # ] > 10 # + 9 &] (* Maciej Ireneusz Wilczynski, Jul 18 2010 *)
Flatten@Position[10*#+{1,3,7,9}&/@Range@4000,{?CompositeQ ..}] (* _Hans Rudolf Widmer, Jul 06 2024 *)

PARI

is(n)=!isprime(10*n+1) && !isprime(10*n+3) && !isprime(10*n+7) && !isprime(10*n+9) \\ Charles R Greathouse IV, Mar 29 2013

Python

from sympy import isprime
def aupto(limit):
  alst = []
  for d in range(2, limit+1):
    td = [10*d + j for j in [1, 3, 7, 9]]
    if not any(isprime(t) for t in td): alst.append(d)
  return alst
print(aupto(342)) # Michael S. Branicky, May 30 2021

Formula

a(n) ~ n. - Charles R Greathouse IV, Mar 29 2013

Extensions

More terms from Miklos Kristof, Aug 27 2002