A231979 - OEIS

%I #8 Nov 19 2013 12:32:24

%S 1,2,4,5,7,8,10,13,17,19,22,29,32,34,37,43,44,50,52,55,65,67,70,77,83,

%T 89,112,113,115,118,124,127,133,145,152,155,167,172,182,188,199,200,

%U 215,229,274,277,295,302,308,322,362,379,400,418,433,488,494,499

%N Numbers n such that for every digit d in n, 2*n + 6*d - 3 is prime.

%C The coefficients 2,6,-3 yield more hits between 1 and 1000000 than 2,2,1 or 1,1,1.

%H T. D. Noe, <a href="/A231979/b231979.txt">Table of n, a(n) for n = 1..2000</a>

%e 124 is in the sequence since

%e   2*124+6*1-3=251 which is prime,

%e   2*124+6*2-3=257 which is prime,

%e   2*124+6*4-3=269 which is prime.

%e 241 is NOT in the sequence since

%e   2*241+6*2-3=491 which is prime,

%e   2*241+6*4-3=503 which is prime,

%e   but 2*241+6*1-3=485 which is not prime.

%t fQ[n_] := Module[{d = IntegerDigits[n]}, And @@ PrimeQ[2*n + 6*d - 3]]; Select[Range[1000], fQ] (* _T. D. Noe_, Nov 19 2013 *)

%o (Java)

%o public class Ndp {

%o // 2n+6d-3 is prime for all digits d in n

%o private static final int MAX = 1000000;

%o public static void main(String[] args) {

%o   String sequence = "";

%o   loop: for (int n = 1; sequence.length() < 250 && n < MAX; n++) {

%o    for (int i = n; i > 0; i /= 10) {

%o     int d = i % 10;

%o     if (!isPrime(2 * n + 6 * d - 3)) {

%o      continue loop;

%o     }

%o    }

%o    sequence += n + ",";

%o   }

%o   System.out.println(sequence);

%o }

%o private static boolean isPrime(long n) {

%o   for (long i = 2; i <= Math.sqrt(n); i++) {

%o    if (n < 2 || n % i == 0) {

%o     return false;

%o    }

%o   }

%o   return true;

%o }

%o }

%K nonn,easy,base

%O 1,2

%A _John R Phelan_, Nov 16 2013